专著：

 

[1]J.Austin Cottrell,Thomas J.R.Hughes,Yuri Bazilevs. ISOGEOMETRIC ANALYSIS, John Wiley & Sons, 2009.

 

[2] Vuong A. Adaptive Hierarchical Isogeometric Finite Element Methods[M]. Springer Science & Business Media, 2012.

 

[3] Jüttler B, Simeon B. Isogeometric Analysis and Applications 2014[M]. Springer, 2016.

 

 

论 文：

 

I.Review

 

[1] Hughes J R, 曹周健, 许志强. 等几何分析[J]. 数学译林. 2011, 30(1): 3.

 

[2] 葛建立, 杨国来, 吕加. 同几何分析研究进展[J]. 力学进展. 2012, 42(6): 771-784.

 

[3] De Lorenzis L, Wriggers P, Hughes T J. Isogeometric contact: a review[J]. GAMM-Mitteilungen. 2014, 37(1): 85-123.

 

[4] 徐岗, 李新, 黄章进, 等. 面向等几何分析的几何计算[J]. 计算机辅助设计与图形学学报. 2015(4): 570-581.

 

[5] 吴紫俊, 黄正东, 左兵权, 等. 等几何分析研究概述[J]. 机械工程学报. 2015, 51(5): 114-129.

 

[6] Nguyen V P, Anitescu C, Bordas S P, et al. Isogeometric analysis: An overview and computer implementation aspects[J]. Mathematics and Computers in Simulation. 2015, 117: 89-116.

 

 

II.几何建模技术

 

1.Splines techniques

 

[1] Uhm T, Kim K, Seo Y, et al. A locally refinable T-spline finite element method for CAD/CAE integration[J]. Structural Engineering and Mechanics. 2008, 30(2): 225-245.

 

[2] Uhm T K, Youn S K. T‐spline finite element method for the analysis of shell structures[J]. International Journal for Numerical Methods in Engineering. 2009, 80(4): 507-536.

 

[3] Bazilevs Y, Calo V M, Cottrell J A, et al. Isogeometric analysis using T-splines[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(5): 229-263.

 

[4] Dörfel M R, Jüttler B, Simeon B. Adaptive isogeometric analysis by local h-refinement with T-splines[J]. Computer methods in applied mechanics and engineering. 2010, 199(5): 264-275.

 

[5] Costantini P, Manni C, Pelosi F, et al. Quasi-interpolation in isogeometric analysis based on generalized B-splines[J]. Computer Aided Geometric Design. 2010, 27(8): 656-668.

 

[6] Buffa A, Cho D, Sangalli G. Linear independence of the T-spline blending functions associated with some particular T-meshes[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(23): 1437-1445.

 

[7] Burkhart D, Hamann B, Umlauf G. Iso-geometric Finite Element Analysis Based on Catmull-Clark : subdivision Solids[J]. Computer Graphics Forum. 2010, 29(5): 1575-1584.

 

[8] Vuong A, Giannelli C, Jüttler B, et al. A hierarchical approach to adaptive local refinement in isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(49): 3554-3567.

 

[9] Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, et al. Rotation free isogeometric thin shell analysis using PHT-splines[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(47): 3410-3424.

 

[10] Nguyen-Thanh N, Nguyen-Xuan H, Bordas S P A, et al. Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(21): 1892-1908.

 

[11] Manni C, Pelosi F, Sampoli M L. Generalized B-splines as a tool in isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(5): 867-881.

 

[12] Da Veiga L B, Buffa A, Cho D, et al. IsoGeometric analysis using T-splines on two-patch geometries[J]. Computer methods in applied mechanics and engineering. 2011, 200(21): 1787-1803.

 

[13] Wang P, Xu J, Deng J, et al. Adaptive isogeometric analysis using rational PHT-splines[J]. Computer-Aided Design. 2011, 43(11): 1438-1448.

 

[14] Qian X, Sigmund O. Isogeometric shape optimization of photonic crystals via Coons patches[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(25): 2237-2255.

 

[15] Tian L, Chen F, Du Q. Adaptive finite element methods for elliptic equations over hierarchical T-meshes[J]. Journal of Computational and Applied Mathematics. 2011, 236(5): 878-891.

 

[16] Li X, Zheng J, Sederberg T W, et al. On linear independence of T-spline blending functions[J]. Computer Aided Geometric Design. 2012, 29(1): 63-76.

 

[17] Giannelli C, Jüttler B, Speleers H. THB-splines: The truncated basis for hierarchical splines[J]. Computer Aided Geometric Design. 2012, 29(7): 485-498.

 

[18] Scott M A, Li X, Sederberg T W, et al. Local refinement of analysis-suitable T-splines[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 213: 206-222.

 

[19] Wu M, Xu J, Wang R, et al. Hierarchical bases of spline spaces with highest order smoothness over hierarchical T-subdivisions[J]. Computer Aided Geometric Design. 2012, 29(7): 499-509.

 

[20] Schumaker L L, Wang L. Approximation power of polynomial splines on T-meshes[J]. Computer Aided Geometric Design. 2012, 29(8): 599-612.

 

[21] Beirão Da Veiga L, Buffa A, Cho D, et al. Analysis-Suitable T-splines are Dual-Compatible[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 249-252: 42-51.

 

[22] Speleers H, Manni C, Pelosi F, et al. Isogeometric analysis with Powell–Sabin splines for advection–diffusion–reaction problems[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 221-222: 132-148.

 

[23] Dokken T, Lyche T, Pettersen K F. Polynomial splines over locally refined box-partitions[J]. Computer Aided Geometric Design. 2013, 30(3): 331-356.

 

[24] Bornemann P B, Cirak F. A subdivision-based implementation of the hierarchical b-spline finite element method[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 253: 584-598.

 

[25] Wang Y, Huang Z, Zheng Y, et al. Isogeometric analysis for compound B-spline surfaces[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 261: 1-15.

 

[26] Wu M, Deng J, Chen F. Dimension of spline spaces with highest order smoothness over hierarchical T-meshes[J]. Computer Aided Geometric Design. 2013, 30(1): 20-34.

 

[27] Beirão Da Veiga L, Buffa A, Sangalli G, et al. Analysis-suitable T-splines of arbitrary degree: definition, linear independence and approximation properties[J]. Mathematical Models and Methods in Applied Sciences. 2013, 23(11): 1979-2003.

 

[28] Johannessen K A, Kvamsdal T, Dokken T. Isogeometric analysis using LR B-splines[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 269: 471-514.

 

[29] Kuru G, Verhoosel C V, Van der Zee K G, et al. Goal-adaptive isogeometric analysis with hierarchical splines[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 270: 270-292.

 

[30] Nguyen-Thanh N, Muthu J, Zhuang X, et al. An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics[J]. Computational Mechanics. 2014, 53(2): 369-385.

 

[31] Scott M A, Thomas D C, Evans E J. Isogeometric spline forests[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 269: 222-264.

 

[32] Li X, Scott M A. Analysis-suitable T-splines: characterization, refineability, and approximation[J]. Mathematical Models and Methods in Applied Sciences. 2014, 24(06): 1141-1164.

 

[33] Giannelli C, Jüttler B, Speleers H. Strongly stable bases for adaptively refined multilevel spline spaces[J]. Advances in Computational Mathematics. 2014, 40(2): 459-490.

 

[34] Kiss G, Giannelli C, Zore U, et al. Adaptive CAD model (re-)construction with THB-splines[J]. Graphical Models. 2014, 76(5): 273-288.

 

[35] Evans E J, Scott M A, Li X, et al. Hierarchical T-splines: Analysis-suitability, Bézier extraction, and application as an adaptive basis for isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 1-20.

 

[36] Berdinsky D, Kim T, Cho D, et al. Bases of T-meshes and the refinement of hierarchical B-splines[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 283: 841-855.

 

[37] Wu Z, Huang Z, Liu Q, et al. A local solution approach for adaptive hierarchical refinement in isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 283: 1467-1492.

 

[38] Jiang W, Dolbow J E. Adaptive refinement of hierarchical B-spline finite elements with an efficient data transfer algorithm[J]. International Journal for Numerical Methods in Engineering. 2015, 102(3-4): 233-256.

 

[39] Johannessen K A, Remonato F, Kvamsdal T. On the similarities and differences between Classical Hierarchical, Truncated Hierarchical and LR B-splines[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 291: 64-101.

 

[40] Johannessen K A, Kumar M, Kvamsdal T. Divergence-conforming discretization for Stokes problem on locally refined meshes using LR B-splines[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 293: 38-70.

 

[41] Giannelli C, Jüttler B, Kleiss S K, et al. THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 299: 337-365.

 

[42] Pan Q, Xu G, Xu G, et al. Isogeometric analysis based on extended Catmull–Clark subdivision[J]. Computers & Mathematics with Applications. 2016, 71(1): 105-119.

 

[43] Buffa A, Giannelli C. Adaptive isogeometric methods with hierarchical splines: error estimator and convergence[J]. Mathematical Models and Methods in Applied Sciences. 2016, 26(01): 1-25.

 

[44] Basappa U, Rajagopal A, Reddy J N. Adaptive Isogeometric Analysis Based on a Combined r-h Strategy[J]. International Journal for Computational Methods in Engineering Science and Mechanics. 2016(just-accepted): 1-55.

 

[45] Liu L, Casquero H, Gomez H, et al. Hybrid-Degree Weighted T-splines and Their Application in Isogeometric Analysis[J]. Computers & Fluids. 2016.

 

[46] Nguyen T, Peters J. Refinable C 1 spline elements for irregular quad layout[J]. Computer Aided Geometric Design. 2016, 43: 123-130.

 

[47] Wei X, Zhang Y J, Hughes T J, et al. Extended Truncated Hierarchical Catmull–Clark Subdivision[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 299: 316-336.

 

[48] Bracco C, Lyche T, Manni C, et al. Generalized spline spaces over T-meshes: Dimension formula and locally refined generalized B-splines[J]. Applied Mathematics and Computation. 2016, 272: 187-198.

 

[49] Tadej Kanduˇc, Carlotta Giannelli, Francesca Pelosic, et al. Adaptive isogeometric analysis with hierarchical box splines[J]. Computer Methods in Applied Mechanics and Engineering, in press.

 

[50] Xuefeng Zhu,Ping Hu,Zheng-Dong Ma. B++ splines with applications to isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 311:503-536.

 

[51] Songtao Xia, Xiaoping Qian. Isogeometric analysis with Bézier tetrahedra[J]. Computer Methods in Applied Mechanics and Engineering, in press

 

[52] Deepesh Toshniwal, Hendrik Speleers, René R. Hiemstra, et al. Multi-degree smooth polar splines: A framework for geometric modeling and isogeometric analysis [J]. Computer Methods in Applied Mechanics and Engineering, in press

 

 

2.Volumetric parameterization

 

[1] Martin T, Cohen E, Kirby R M. Volumetric parameterization and trivariate B-spline fitting using harmonic functions[J]. Computer Aided Geometric Design. 2009, 26(6): 648-664.

 

[2] Martin T, Cohen E. Volumetric parameterization of complex objects by respecting multiple materials[J]. Computers & Graphics. 2010, 34(3): 187-197.

 

[3] Cohen E, Martin T, Kirby R M, et al. Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(5): 334-356.

 

[4] Xu G, Mourrain B, Duvigneau R, et al. Parameterization of computational domain in isogeometric analysis: methods and comparison[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(23): 2021-2031.

 

[5] Wang W, Zhang Y, Scott M A, et al. Converting an unstructured quadrilateral mesh to a standard T-spline surface[J]. Computational Mechanics. 2011, 48(4): 477-498.

 

[6] Takacs T, Jüttler B. Existence of stiffness matrix integrals for singularly parameterized domains in isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(49): 3568-3582.

 

[7] Escobar J M, Cascón J M, Rodríguez E, et al. A new approach to solid modeling with trivariate T-splines based on mesh optimization[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(45): 3210-3222.

 

[8] Zhang Y, Wang W, Hughes T J. Solid T-spline construction from boundary representations for genus-zero geometry[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 249: 185-197.

 

[9] Takacs T, Jüttler B. H2 regularity properties of singular parameterizations in isogeometric analysis[J]. Graphical models. 2012, 74(6): 361-372.

 

[10] Hesch C, Betsch P. Isogeometric analysis and domain decomposition methods[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 213: 104-112.

 

[11] Da Veiga L B, Buffa A, Cho D, et al. Analysis-suitable T-splines are dual-compatible[J]. Computer methods in applied mechanics and engineering. 2012, 249: 42-51.

 

[12] 张勇, 林皋, 胡志强. 等几何分析方法中重控制点问题的研究与应用[J]. 工程力学. 2013, 30(2): 1-7.

 

[13] 许华强, 徐岗, 胡维华, et al. 面向等几何分析的B样条参数体生成方法[J]. 图学学报. 2013, 34(3): 43-48.

 

[14] Zhu X, Hu P, Ma Z, et al. A new surface parameterization method based on one-step inverse forming for isogeometric analysis-suited geometry[J]. The International Journal of Advanced Manufacturing Technology. 2013, 65(9-12): 1215-1227.

 

[15] Zhang Y, Wang W, Hughes T J. Conformal solid T-spline construction from boundary T-spline representations[J]. Computational Mechanics. 2013, 51(6): 1051-1059.

 

[16] Xu G, Mourrain B, Duvigneau R, et al. Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications[J]. Computer-Aided Design. 2013, 45(2): 395-404.

 

[17] Xu G, Mourrain B, Duvigneau R, et al. Optimal analysis-aware parameterization of computational domain in 3D isogeometric analysis[J]. Computer-Aided Design. 2013, 45(4): 812-821.

 

[18] Xu G, Mourrain B, Duvigneau R, et al. Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method[J]. Journal of Computational Physics. 2013, 252: 275-289.

 

[19] Wang W, Zhang Y, Liu L, et al. Trivariate solid T-spline construction from boundary triangulations with arbitrary genus topology[J]. Computer-Aided Design. 2013, 45(2): 351-360.

 

[20] Evans J A, Hughes T J R. Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements[J]. Numerische Mathematik. 2013, 123(2): 259-290.

 

[21] Yuan X, Ma W. Mapped B-spline basis functions for shape design and isogeometric analysis over an arbitrary parameterization[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 269: 87-107.

 

[22] Xu G, Mourrain B, Galligo A, et al. High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods[J]. Computational Mechanics. 2014, 54(5): 1303-1313.

 

[23] Wang X, Qian X. An optimization approach for constructing trivariate B-spline solids[J]. Computer-Aided Design. 2014, 46: 179-191.

 

[24] Pilgerstorfer E, Jüttler B. Bounding the influence of domain parameterization and knot spacing on numerical stability in Isogeometric Analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 268: 589-613.

 

[25] Nguyen V P, Kerfriden P, Bordas S P, et al. Isogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithm[J]. Computer-Aided Design. 2014, 55: 49-63.

 

[26] Nguyen D, Pauley M, Jüttler B. Isogeometric segmentation. Part II: On the segmentability of contractible solids with non-convex edges[J]. Graphical Models. 2014, 76(5): 426-439.

 

[27] Liu L, Zhang Y, Hughes T J, et al. Volumetric T-spline construction using Boolean operations[J]. Engineering with Computers. 2014, 30(4): 425-439.

 

[28] Jüttler B, Kapl M, Nguyen D, et al. Isogeometric segmentation: The case of contractible solids without non-convex edges[J]. Computer-Aided Design. 2014, 57: 74-90.

 

[29] Jaxon N, Qian X. Isogeometric analysis on triangulations[J]. Computer-Aided Design. 2014, 46: 45-57.

 

[30] Escobar J M, Montenegro R, Rodríguez E, et al. The meccano method for isogeometric solid modeling and applications[J]. Engineering with computers. 2014, 30(3): 331-343.

 

[31] Brovka M, López J I, Escobar J M, et al. A new method for T-spline parameterization of complex 2D geometries[J]. Engineering with Computers. 2014, 30(4): 457-473.

 

[32] Brovka M, López J I, Escobar J M, et al. Construction of polynomial spline spaces over quadtree and octree T-meshes[J]. Procedia Engineering. 2014, 82: 21-33.

 

[33] Speleers H, Manni C. Optimizing domain parameterization in isogeometric analysis based on Powell–Sabin splines[J]. Journal of Computational and Applied Mathematics. 2015, 289: 68-86.

 

[34] Groisser D, Peters J. Matched Gk-constructions always yield Ck-continuous isogeometric elements[J]. Computer aided geometric design. 2015, 34: 67-72.

 

[35] Choi M, Cho S. A mesh regularization scheme to update internal control points for isogeometric shape design optimization[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 285: 694-713.

 

[36] Hosseini S F, Moetakef-Imani B, Hadidi-Moud S, et al. The effect of parameterization on isogeometric analysis of free-form curved beams[J]. Acta Mechanica. 2016: 1-16.

 

[37] 陈龙，阮辰，韩文瑜. 非均质NURBS体参数化模型切片算法[J]. 系统仿真学报, 2016, 28(10):2431-2447.

 

 

3.Trimmed surface

 

[1] Kim H, Seo Y, Youn S. Isogeometric analysis for trimmed CAD surfaces[J]. Computer Methods in Applied Mechanics and Engineering. 2009, 198(37): 2982-2995.

 

 

[2] Kim H, Seo Y, Youn S. Isogeometric analysis with trimming technique for problems of arbitrary complex topology[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(45): 2796-2812.

 

[3] Seo Y, Kim H, Youn S. Isogeometric topology optimization using trimmed spline surfaces[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(49): 3270-3296.

 

[4] Schmidt R, Wüchner R, Bletzinger K. Isogeometric analysis of trimmed NURBS geometries[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 241: 93-111.

 

[5] Ruess M, Schillinger D, özcan A I, et al. Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 269: 46-71.

 

[6] Nagy A P, Benson D J. On the numerical integration of trimmed isogeometric elements[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 165-185.

 

[7] Beer G, Marussig B, Zechner J. A simple approach to the numerical simulation with trimmed CAD surfaces[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 285: 776-790.

 

[8] Kang P, Youn S. Isogeometric analysis of topologically complex shell structures[J]. Finite Elements in Analysis and Design. 2015, 99: 68-81.

 

 

4.CSG model

 

[1] Zuo B, Huang Z, Wang Y, et al. Isogeometric analysis for CSG models[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 285: 102-124.

 

 

5.Multi NURBS Patches

 

[1] Kleiss S K, Pechstein C, Jüttler B, et al. IETI–isogeometric tearing and interconnecting[J]. Computer methods in applied mechanics and engineering. 2012, 247: 201-215.

 

[2] Hesch C, Betsch P. Isogeometric analysis and domain decomposition methods[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 213-216: 104-112.

 

[3] Apostolatos A, Schmidt R, Wüchner R, et al. A Nitsche‐type formulation and comparison of the most common domain decomposition methods in isogeometric analysis[J]. International Journal for Numerical Methods in Engineering. 2014, 97(7): 473-504.

 

[4] Greco L, Cuomo M. An implicit G1 multi patch B-spline interpolation for Kirchhoff–Love space rod[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 269: 173-197.

 

[5] Nguyen V P, Kerfriden P, Brino M, et al. Nitsche’s method for two and three dimensional NURBS patch coupling[J]. Computational Mechanics. 2014, 53(6): 1163-1182.

 

[6] Dornisch W, Vitucci G, Klinkel S. The weak substitution method–an application of the mortar method for patch coupling in NURBS‐based isogeometric analysis[J]. International Journal for Numerical Methods in Engineering. 2015, 103(3): 205-234.

 

[7] Kapl M, Vitrih V, Jüttler B, et al. Isogeometric analysis with geometrically continuous functions on two-patch geometries[J]. Computers & Mathematics with Applications. 2015, 70(7): 1518-1538.

 

[8] Guo Y, Ruess M. Nitsche’s method for a coupling of isogeometric thin shells and blended shell structures[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 881-905.

 

[9] Breitenberger M, Apostolatos A, Philipp B, et al. Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 401-457.

 

[10] Du X, Zhao G, Wang W. Nitsche method for isogeometric analysis of Reissner–Mindlin plate with non-conforming multi-patches[J]. Computer Aided Geometric Design. 2015, 35-36: 121-136.

 

[11] Buchegger F, Jüttler B, Mantzaflaris A. Adaptively refined multi-patch B-splines with enhanced smoothness[J]. Applied Mathematics and Computation. 2016, 272: 159-172.

 

 

III.力学分析

 

1.Error estimate

 

[1] Bazilevs Y, Beirao Da Veiga L, Cottrell J A, et al. Isogeometric analysis: approximation, stability and error estimates for h-refined meshes[J]. Mathematical Models and Methods in Applied Sciences. 2006, 16(07): 1031-1090.

 

[2] Cottrell J A, Hughes T, Reali A. Studies of refinement and continuity in isogeometric structural analysis[J]. Computer methods in applied mechanics and engineering. 2007, 196(41): 4160-4183.

 

[3] Akkerman I, Bazilevs Y, Calo V M, et al. The role of continuity in residual-based variational multiscale modeling of turbulence[J]. Computational Mechanics. 2008, 41(3): 371-378.

 

[4] Hughes T J R, Reali A, Sangalli G. Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: Comparison of p-method finite elements with k-method NURBS[J]. Computer Methods in Applied Mechanics and Engineering. 2008, 197(49-50): 4104-4124.

 

[5] Evans J A, Bazilevs Y, Babuška I, et al. n-Widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method[J]. Computer Methods in Applied Mechanics and Engineering. 2009, 198(21): 1726-1741.

 

[6] Da Veiga L B, Buffa A, Rivas J, et al. Some estimates for h–p–k-refinement in Isogeometric Analysis[J]. Numerische Mathematik. 2011, 118(2): 271-305.

 

[7] Van der Zee K G, Verhoosel C V. Isogeometric analysis-based goal-oriented error estimation for free-boundary problems[J]. Finite Elements in Analysis and Design. 2011, 47(6): 600-609.

 

[8] 徐岗, 王毅刚, 胡维华. 等几何分析中的 rp 型细化方法[J]. 计算机辅助设计与图形学学报. 2011, 23(12): 2019-2024.

 

[9] Collier N, Pardo D, Dalcin L, et al. The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 213: 353-361.

 

[10] Da Veiga L B, Cho D, Sangalli G. Anisotropic NURBS approximation in isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 209: 1-11.

 

[11] Dedè L, Santos H A F A. B-spline goal-oriented error estimators for geometrically nonlinear rods[J]. Computational Mechanics. 2012, 49(1): 35-52.

 

[12] Hassani B, Ganjali A, Tavakkoli M. An isogeometrical approach to error estimation and stress recovery[J]. European Journal of Mechanics-A/Solids. 2012, 31(1): 101-109.

 

[13] Xu G, Mourrain B, Duvigneau R, et al. A New Error Assessment Method in Isogeometric Analysis of 2D Heat Conduction Problems[J]. Advanced Science Letters. 2012, 10(1): 508-512.

 

[14] Da Veiga L B, Buffa A, Sangalli G, et al. Mathematical analysis of variational isogeometric methods[J]. Acta Numerica. 2014, 23: 157-287.

 

[15] Hughes T J R, Evans J A, Reali A. Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 272: 290-320.

 

[16] Kumar M, Kvamsdal T, Johannessen K A. Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis[J]. Submitted to Computer methods in applied mechanics and engineering. 2014.

 

[17] Tagliabue A, Dedè L, Quarteroni A. Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics[J]. Computers & Fluids. 2014, 102: 277-303.

 

[18] 徐岗, 朱亚光, 邓立山, et al. 局部误差驱动的等几何分析计算域自适应优化方法[J]. 计算机辅助设计与图形学学报. 2014, 26(10): 1633-1638.

 

[19] Dedè L, Quarteroni A. Isogeometric Analysis for second order Partial Differential Equations on surfaces[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 807-834.

 

[20] Kleiss S K, Tomar S K. Guaranteed and sharp a posteriori error estimates in isogeometric analysis[J]. Computers & Mathematics with Applications. 2015, 70(3): 167-190.

 

[21] Buffa A, Giannelli C. Adaptive isogeometric methods with hierarchical splines: error estimator and convergence[J]. Mathematical Models and Methods in Applied Sciences. 2016, 26(01): 1-25.

 

[22] Mukesh Kumar, Trond Kvamsdal, Kjetil Andr´e Johannessen. Superconvergent patch recovery and a posteriori error estimation[J]. Computer Methods in Applied Mechanics and Engineering, in press

 

[23] Gábor Hénap, László Szabó. On the configurational-force-based r-adaptive mesh refinement in isogeometric analysis [J]. Finite Elements in Analysis and Design, 2017, 124:1-6.

 

 

2.Impose Dirichlet boundary conditionDynamics

 

[1] Bazilevs Y, Michler C, Calo V M, et al. Weak Dirichlet boundary conditions for wall-bounded turbulent flows[J]. Computer Methods in Applied Mechanics and Engineering. 2007, 196(49): 4853-4862.

 

[2] Bazilevs Y, Hughes T J. Weak imposition of Dirichlet boundary conditions in fluid mechanics[J]. Computers & Fluids. 2007, 36(1): 12-26.

 

[3] Costantini P, Manni C, Pelosi F, et al. Quasi-interpolation in isogeometric analysis based on generalized B-splines[J]. Computer Aided Geometric Design. 2010, 27(8): 656-668.

 

[4] Embar A, Dolbow J, Harari I. Imposing Dirichlet boundary conditions with Nitsche's method and spline‐based finite elements[J]. International Journal for Numerical Methods in Engineering. 2010, 83(7): 877-898.

 

[5] Wang D, Xuan J. An improved NURBS-based isogeometric analysis with enhanced treatment of essential boundary conditions[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(37): 2425-2436.

 

[6] Ghorashi S S, Valizadeh N, Mohammadi S. Extended isogeometric analysis for simulation of stationary and propagating cracks[J]. International Journal for Numerical Methods in Engineering. 2012, 89(9): 1069-1101.

 

[7] Shojaee S, Izadpenah E, Haeri A. Imposition of essential boundary conditions in isogeometric analysis using the lagrange multiplier method[J]. International Journal of Optimization in Civil Engineering,(2). 2012: 247-271.

 

[8] 陈涛, 莫蓉, 万能. 等几何分析中Dirichlet边界条件的配点施加方法[J]. 机械工程学报. 2012(05): 157-164.

 

[9] 陈涛, 莫蓉, 万能, et al. 等几何分析中采用 Nitsche 法施加位移边界条件[J]. 力学学报. 2012, 44(2): 371-381.

 

[10] 王东东, 轩军厂, 张灿辉. 几何精确 NURBS 有限元中边界条件施加方式对精度影响的三维计算分析[J]. 计算力学学报. 2012, 29(1): 31-37.

 

[11] 祝雪峰, 马正东, 胡平. 几何精确非协调等几何 NURBS 有限元[J]. 固体力学学报. 2012, 33(5): 487-492.

 

[12] Lu J, Yang G, Ge J. Blending NURBS and Lagrangian representations in isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 257: 117-125.

 

[13] Ge J, Guo B, Yang G, et al. Blending isogeometric and Lagrangian elements in three-dimensional analysis[J]. Finite Elements in Analysis and Design. 2016, 112: 50-63.

 

 

3.Quadrature method

 

[1] Hughes T J, Reali A, Sangalli G. Efficient quadrature for NURBS-based isogeometric analysis[J]. Computer methods in applied mechanics and engineering. 2010, 199(5): 301-313.

 

[2] Auricchio F, Calabro F, Hughes T, et al. A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 249: 15-27.

 

[3] Rypl D, Patzák B. Study of computational efficiency of numerical quadrature schemes in the isogeometric analysis[J]. Engineering Mechanics. 2012: 304.

 

[4] Wang D, Zhang H, Xuan J. A strain smoothing formulation for NURBS-based isogeometric finite element analysis[J]. Science China Physics, Mechanics and Astronomy. 2012, 55(1): 132-140.

 

[5] Schillinger D, Hossain S J, Hughes T J. Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 277: 1-45.

 

[6] Adam C, Bouabdallah S, Zarroug M, et al. Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 279: 1-28.

 

[7] Adam C, Hughes T, Bouabdallah S, et al. Selective and reduced numerical integrations for NURBS-based isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 732-761.

 

[8] Hillman M, Chen J S, Bazilevs Y. Variationally consistent domain integration for isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 521-540.

 

[9] Nagy A P, Benson D J. On the numerical integration of trimmed isogeometric elements[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 165-185.

 

[10] Adam C, Bouabdallah S, Zarroug M, et al. Improved numerical integration for locking treatment in isogeometric structural elements. Part II: Plates and shells[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 106-137.

 

[11] Vignollet J, May S, Borst R. On the numerical integration of isogeometric interface elements[J]. International Journal for Numerical Methods in Engineering. 2015, 102(11): 1733-1749.

 

[12] Mantzaflaris A, Jüttler B. Integration by interpolation and look-up for Galerkin-based isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 373-400.

 

[13] Bartoň M, Calo V M. Optimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 305: 217-240.

 

[14] Jüttler B, Mantzaflaris A, Perl R, et al. On numerical integration in isogeometric subdivision methods for PDEs on surfaces[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

 

4.Bézier extraction operation

 

[1] Borden M J, Scott M A, Evans J A, et al. Isogeometric finite element data structures based on Bézier extraction of NURBS[J]. International Journal for Numerical Methods in Engineering. 2011, 87(1‐5): 15-47.

 

[2] Scott M A, Borden M J, Verhoosel C V, et al. Isogeometric finite element data structures based on Bézier extraction of T-plines[J]. International Journal for Numerical Methods in Engineering. 2011, 88(2): 126-156.

 

[3] Irzal F, Remmers J, Verhoosel C V, et al. An isogeometric analysis Bézier interface element for mechanical and poromechanical fracture problems[J]. International Journal for Numerical Methods in Engineering. 2014, 97(8): 608-628.

 

[4] Evans E J, Scott M A, Li X, et al. Hierarchical T-splines: Analysis-suitability, Bézier extraction, and application as an adaptive basis for isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 1-20.

 

[5] Thomas D C, Scott M A, Evans J A, et al. Bézier projection: a unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 55-105.

 

[6] Hennig P, Müller S, Kästner M. Bézier extraction and adaptive refinement of truncated hierarchical NURBS[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

 

5.IGA program design

 

[1] Vuong A, Heinrich C, Simeon B. ISOGAT: a 2D tutorial MATLAB code for Isogeometric Analysis[J]. Computer Aided Geometric Design. 2010, 27(8): 644-655.

 

[2] De Falco C, Reali A, Vázquez R. GeoPDEs: a research tool for Isogeometric Analysis of PDEs[J]. Advances in Engineering Software. 2011, 42(12): 1020-1034.

 

[3] Rypl D, Patzák B. From the finite element analysis to the isogeometric analysis in an object oriented computing environment[J]. Advances in Engineering Software. 2012, 44(1): 116-125.

 

[4] Rypl D, Patzák B. Object oriented implementation of the T-spline based isogeometric analysis[J]. Advances in Engineering Software. 2012, 50: 137-149.

 

[5] Pauletti M S, Martinelli M, Cavallini N, et al. Igatools: An isogeometric analysis library[J]. SIAM Journal on Scientific Computing. 2015, 37(4): C465-C496.

 

[6] Hsu M, Wang C, Herrema A J, et al. An interactive geometry modeling and parametric design platform for isogeometric analysis[J]. Computers & Mathematics with Applications. 2015, 70(7): 1481-1500.

 

 

6.Preconditioners

 

[1] Da Veiga L B, Cho D, Pavarino L F, et al. Overlapping Schwarz methods for isogeometric analysis[J]. SIAM Journal on Numerical Analysis. 2012, 50(3): 1394-1416.

 

[2] Beirão Da Veiga L, Cho D, Pavarino L F, et al. BDDC preconditioners for isogeometric analysis[J]. Mathematical Models and Methods in Applied Sciences. 2013, 23(06): 1099-1142.

 

[3] Buffa A, Harbrecht H, Kunoth A, et al. BPX-preconditioning for isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 265: 63-70.

 

[4] Gahalaut K, Tomar S K, Kraus J K. Algebraic multilevel preconditioning in isogeometric analysis: Construction and numerical studies[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 266: 40-56.

 

[5] Da Veiga L B, Cho D, Pavarino L F, et al. Isogeometric Schwarz preconditioners for linear elasticity systems[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 253: 439-454.

 

[6] Gahalaut K P S, Kraus J K, Tomar S K. Multigrid methods for isogeometric discretization[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 253: 413-425.

 

[7] Da Veiga L B, Pavarino L F, Scacchi S, et al. Isogeometric BDDC preconditioners with deluxe scaling[J]. SIAM Journal on Scientific Computing. 2014, 36(3): A1118-A1139.

 

 

7.High performance solver

 

[1] Hsu M, Akkerman I, Bazilevs Y. High-performance computing of wind turbine aerodynamics using isogeometric analysis[J]. Computers & Fluids. 2011, 49(1): 93-100.

 

[2] Kuźnik K, Paszyński M, Calo V. Graph grammar-based multi-frontal parallel direct solver for two-dimensional isogeometric analysis[J]. Procedia Computer Science. 2012, 9: 1454-1463.

 

[3] Pardo D, Paszynski M, Collier N, et al. A survey on direct solvers for Galerkin methods[J]. SeMA Journal. 2012, 57(1): 107-134.

 

[4] Collier N, Dalcin L, Pardo D, et al. The cost of continuity: performance of iterative solvers on isogeometric finite elements[J]. SIAM Journal on Scientific Computing. 2013, 35(2): A767-A784.

 

[5] Kuźnik K, Paszyński M, Calo V. Grammar-Based Multi-Frontal Solver for One Dimensional Isogeometric Analysis with Multiple Right-Hand-Sides[J]. Procedia Computer Science. 2013, 18: 1574-1583.

 

[6] Kuźnik K, Paszyński M, Calo V. Grammar based multi-frontal solver for isogeometric analysis in 1d[J]. Computer Science. 2013, 14(4)): 589-613.

 

[7] Gahalaut K, Kraus J K, Tomar S K. Multigrid methods for isogeometric discretization[J]. Computer methods in applied mechanics and engineering. 2013, 253: 413-425.

 

[8] Rypl D, Patzák B. Construction of weighted dual graphs of NURBS-based isogeometric meshes[J]. Advances in Engineering Software. 2013, 60-61: 31-41.

 

[9] Bernal L M, Calo V M, Collier N, et al. Isogeometric Analysis of Hyperelastic Materials Using PetIGA[J]. Procedia Computer Science. 2013, 18: 1604-1613.

 

[10] 郭利财, 黄章进, 顾乃杰. 一种用计算域分解的等几何分析并行化方法[J]. 小型微型计算机系统. 2013, 34(6): 1396-1399.

 

[11] Garoni C, Manni C, Pelosi F, et al. On the spectrum of stiffness matrices arising from isogeometric analysis[J]. Numerische Mathematik. 2014, 127(4): 751-799.

 

[12] Karatarakis A, Karakitsios P, Papadrakakis M. GPU accelerated computation of the isogeometric analysis stiffness matrix[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 269: 334-355.

 

[13] Collier N, Dalcin L, Calo V M. On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers[J]. International Journal for Numerical Methods in Engineering. 2014, 100(8): 620-632.

 

[14] Woźniak M, Kuźnik K, Paszyński M, et al. Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers[J]. Computers & Mathematics with Applications. 2014, 67(10): 1864-1883.

 

[15] 刘石, 陈德祥, 冯永新, 等. 等几何分析的多重网格共轭梯度法[J]. 应用数学和力学. 2014, 35(6): 630-639.

 

[16] Mantzaflaris A, Jüttler B. Integration by interpolation and look-up for Galerkin-based isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 373-400.

 

[17] Antolin P, Buffa A, Calabro F, et al. Efficient matrix computation for tensor-product isogeometric analysis: The use of sum factorization[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 285: 817-828.

 

[18] Donatelli M, Garoni C, Manni C, et al. Robust and optimal multi-iterative techniques for IgA collocation linear systems[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 1120-1146.

 

[19] Woźniak M. Fast GPU integration algorithm for isogeometric finite element method solvers using task dependency graphs[J]. Journal of Computational Science. 2015, 11: 145-152.

 

 

8.Biomechanics

 

[1] Zhang Y, Bazilevs Y, Goswami S, et al. Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow[J]. Computer methods in applied mechanics and engineering. 2007, 196(29): 2943-2959.

 

[2] Isaksen J G, Bazilevs Y, Kvamsdal T, et al. Determination of wall tension in cerebral artery aneurysms by numerical simulation[J]. Stroke. 2008, 39(12): 3172-3178.

 

[3] Bazilevs Y, Gohean J R, Hughes T J R, et al. Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device[J]. Computer Methods in Applied Mechanics and Engineering. 2009, 198(45-46): 3534-3550.

 

[4] Hossain S S, Hossainy S F A, Bazilevs Y, et al. Mathematical modeling of coupled drug and drug-encapsulated nanoparticle transport in patient-specific coronary artery walls[J]. Computational Mechanics. 2012, 49(2): 213-242.

 

[5] Takizawa K, Schjodt K, Puntel A, et al. Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent[J]. Computational Mechanics. 2012, 50(6): 675-686.

 

[6] Hossain S S, Zhang Y, Liang X, et al. In silico vascular modeling for personalized nanoparticle delivery[J]. Nanomedicine. 2013, 8(3): 343-357.

 

[7] Chivukula V, Mousel J, Lu J, et al. Micro-scale blood particulate dynamics using a non-uniform rational B-spline-based isogeometric analysis[J]. International Journal for Numerical Methods in Biomedical Engineering. 2014, 30(12): 1437-1459.

 

[8] Tepole A B, Gart M, Gosain A K, et al. Characterization of living skin using multi-view stereo and isogeometric analysis[J]. Acta biomaterialia. 2014, 10(11): 4822-4831.

 

[9] Auricchio F, Conti M, Ferraro M, et al. Innovative and efficient stent flexibility simulations based on isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 295: 347-361.

 

[10] Hsu M, Kamensky D, Xu F, et al. Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models[J]. Computational mechanics. 2015, 55(6): 1211-1225.

 

[11] Morganti S, Auricchio F, Benson D J, et al. Patient-specific isogeometric structural analysis of aortic valve closure[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 508-520.

 

[12] Verhoosel C V, Van Zwieten G J, Van Rietbergen B, et al. Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 138-164.

 

[13] 高建伟, 陈龙. 基于等几何分析的股骨模型静力学分析[J]. 计算机仿真. 2015, 32(5): 340-343.

 

 

9.Contact problem

 

[1] De Lorenzis L, Temizer I, Wriggers P, et al. A large deformation frictional contact formulation using NURBS‐based isogeometric analysis[J]. International Journal for Numerical Methods in Engineering. 2011, 87(13): 1278-1300.

 

[2] Lu J. Isogeometric contact analysis: Geometric basis and formulation for frictionless contact[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(5): 726-741.

 

[3] Temizer I, Wriggers P, Hughes T. Contact treatment in isogeometric analysis with NURBS[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(9): 1100-1112.

 

[4] De Lorenzis L, Wriggers P, Zavarise G. A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method[J]. Computational Mechanics. 2012, 49(1): 1-20.

 

[5] Kim J Y, Youn S K. Isogeometric contact analysis using mortar method[J]. International Journal for Numerical Methods in Engineering. 2012, 89(12): 1559-1581.

 

[6] Temizer I, Wriggers P, Hughes T. Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 209: 115-128.

 

[7] Matzen M E, Cichosz T, Bischoff M. A point to segment contact formulation for isogeometric, NURBS based finite elements[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 255: 27-39.

 

[8] Dimitri R, De Lorenzis L, Scott M A, et al. Isogeometric large deformation frictionless contact using T-splines[J]. Computer methods in applied mechanics and engineering. 2014, 269: 394-414.

 

[9] Dittmann M, Franke M, Temizer I, et al. Isogeometric Analysis and thermomechanical Mortar contact problems[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 274: 192-212.

 

[10] Temizer I. Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis[J]. International Journal for Numerical Methods in Engineering. 2014, 97(8): 582-607.

 

[11] Temizer İ. Computational homogenization of soft matter friction: Isogeometric framework and elastic boundary layers[J]. International Journal for Numerical Methods in Engineering. 2014, 100(13): 953-981.

 

[12] Temizer İ, Abdalla M M, Gürdal Z. An interior point method for isogeometric contact[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 276: 589-611.

 

[13] Brivadis E, Buffa A, Wohlmuth B, et al. Isogeometric mortar methods[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 292-319.

 

[14] 许欢, 杨国来, 郑建国, et al. 齿轮无摩擦接触的等几何分析研究[J]. 机械传动. 2015, 39(5): 30-32.

 

[15] Seitz A, Farah P, Kremheller J, et al. Isogeometric dual mortar methods for computational contact mechanics[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

[16] Temizer İ, Hesch C. Hierarchical NURBS in frictionless contact[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 299: 161-186.

 

 

10.Crack

 

[1] Benson D J, Bazilevs Y, De Luycker E, et al. A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM[J]. International Journal for Numerical Methods in Engineering. 2010, 83(6): 765-785.

 

[2] De Luycker E, Benson D J, Belytschko T, et al. X‐FEM in isogeometric analysis for linear fracture mechanics[J]. International Journal for Numerical Methods in Engineering. 2011, 87(6): 541-565.

 

[3] Verhoosel C V, Scott M A, De Borst R, et al. An isogeometric approach to cohesive zone modeling[J]. International Journal for Numerical Methods in Engineering. 2011, 87(1‐5): 336-360.

 

[4] Ghorashi S S, Valizadeh N, Mohammadi S. Extended isogeometric analysis for simulation of stationary and propagating cracks[J]. International Journal for Numerical Methods in Engineering. 2012, 89(9): 1069-1101.

 

[5] Tambat A, Subbarayan G. Isogeometric enriched field approximations[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 245: 1-21.

 

[6] Borden M J, Verhoosel C V, Scott M A, et al. A phase-field description of dynamic brittle fracture[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 217-220: 77-95.

 

[7] Jeong J W, Oh H, Kang S, et al. Mapping techniques for isogeometric analysis of elliptic boundary value problems containing singularities[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 254: 334-352.

 

[8] Nguyen V P, Nguyen-Xuan H. High-order B-splines based finite elements for delamination analysis of laminated composites[J]. Composite Structures. 2013, 102: 261-275.

 

[9] Shojaee S, Ghelichi M, Izadpanah E. Combination of isogeometric analysis and extended finite element in linear crack analysis[J]. Structural Engineering and Mechanics. 2013, 48(1): 125-150.

 

[10] Borden M J, Hughes T J, Landis C M, et al. A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 273: 100-118.

 

[11] Irzal F, Remmers J, Verhoosel C V, et al. An isogeometric analysis Bézier interface element for mechanical and poromechanical fracture problems[J]. International Journal for Numerical Methods in Engineering. 2014, 97(8): 608-628.

 

[12] Oh H S, Kim H, Jeong J W. Enriched isogeometric analysis of elliptic boundary value problems in domains with cracks and/or corners[J]. International Journal for Numerical Methods in Engineering. 2014, 97(3): 149-180.

 

[13] Nguyen-Xuan H, Tran L V, Thai C H, et al. Plastic collapse analysis of cracked structures using extended isogeometric elements and second-order cone programming[J]. Theoretical and Applied Fracture Mechanics. 2014, 72: 13-27.

 

[14] Berger-Vergiat L, Mcauliffe C, Waisman H. Isogeometric analysis of shear bands[J]. Computational Mechanics. 2014, 54(2): 503-521.

 

[15] Cuomo M, Contrafatto L, Greco L. A variational model based on isogeometric interpolation for the analysis of cracked bodies[J]. International Journal of Engineering Science. 2014, 80: 173-188.

 

[16] Nguyen V P, Kerfriden P, Bordas S P. Two-and three-dimensional isogeometric cohesive elements for composite delamination analysis[J]. Composites Part B: Engineering. 2014, 60: 193-212.

 

[17] Shojaee S, Asgharzadeh M, Haeri A. Crack analysis in orthotropic media using combination of isogeometric analysis and extended finite element[J]. International Journal of Applied Mechanics. 2014, 6(06): 1450068.

 

[18] Dimitri R, De Lorenzis L, Wriggers P, et al. NURBS-and T-spline-based isogeometric cohesive zone modeling of interface debonding[J]. Computational Mechanics. 2014, 54(2): 369-388.

 

[19] Upreti K, Song T, Tambat A, et al. Algebraic distance estimations for enriched isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 280: 28-56.

 

[20] Amiri F, Millán D, Shen Y, et al. Phase-field modeling of fracture in linear thin shells[J]. Theoretical and Applied Fracture Mechanics. 2014, 69: 102-109.

 

[21] Choi M, Cho S. Isogeometric shape design sensitivity analysis of stress intensity factors for curved crack problems[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 279: 469-496.

 

[22] Guo Y, Ruess M, Gürdal Z. A contact extended isogeometric layerwise approach for the buckling analysis of delaminated composites[J]. Composite Structures. 2014, 116: 55-66.

 

[23] Jia Y, Anitescu C, Ghorashi S S, et al. Extended isogeometric analysis for material interface problems[J]. IMA Journal of Applied Mathematics. 2015, 80(3): 608-633.

 

[24] Ghorashi S S, Valizadeh N, Mohammadi S, et al. T-spline based XIGA for fracture analysis of orthotropic media[J]. Computers & Structures. 2015, 147: 138-146.

 

[25] Nguyen-Thanh N, Valizadeh N, Nguyen M N, et al. An extended isogeometric thin shell analysis based on Kirchhoff–Love theory[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 265-291.

 

[26] Langer U, Mantzaflaris A, Moore S E, et al. Mesh grading in isogeometric analysis[J]. Computers & Mathematics with Applications. 2015, 70(7): 1685-1700.

 

[27] Bayesteh H, Afshar A, Mohammdi S. Thermo-mechanical fracture study of inhomogeneous cracked solids by the extended isogeometric analysis method[J]. European Journal of Mechanics-A/Solids. 2015, 51: 123-139.

 

[28] Tran L V, Ly H A, Lee J, et al. Vibration analysis of cracked FGM plates using higher-order shear deformation theory and extended isogeometric approach[J]. International Journal of Mechanical Sciences. 2015, 96: 65-78.

 

[29] Bui T Q. Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 295: 470-509.

 

[30] Bhardwaj G, Singh I V, Mishra B K. Stochastic fatigue crack growth simulation of interfacial crack in bi-layered FGMs using XIGA[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 186-229.

 

[31] Bhardwaj G, Singh I V, Mishra B K, et al. Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions[J]. Composite Structures. 2015, 126: 347-359.

 

[32] Song T, Upreti K, Subbarayan G. A sharp interface isogeometric solution to the Stefan problem[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 556-582.

 

[33] Hosseini S, Remmers J J C, Verhoosel C V, et al. Propagation of delamination in composite materials with isogeometric continuum shell elements[J]. International Journal for Numerical Methods in Engineering. 2015, 102(3-4): 159-179.

 

[34] Yu T, Bui T Q, Yin S, et al. On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis[J]. Composite Structures. 2016, 136: 684-695.

 

[35] Vignollet J, May S, Borst R D. Isogeometric analysis of fluid‐saturated porous media including flow in the cracks[J]. International Journal for Numerical Methods in Engineering. 2016.

 

[36] Bui T Q, Hirose S, Zhang C, et al. Extended isogeometric analysis for dynamic fracture in multiphase piezoelectric/piezomagnetic composites[J]. Mechanics of Materials. 2016, 97: 135-163.

 

[37] Bhardwaj G, Singh I V, Mishra B K, et al. Numerical simulations of cracked plate using XIGA under different loads and boundary conditions[J]. Mechanics of Advanced Materials and Structures. 2016, 23(6): 704-714.

 

 

11.DIC(Digital Image Correlation)

 

[1] Réthoré J, Elguedj T, Simon P, et al. On the use of NURBS functions for displacement derivatives measurement by digital image correlation[J]. Experimental Mechanics. 2010, 50(7): 1099-1116.

 

[2] Elguedj T, Réthoré J, Buteri A. Isogeometric analysis for strain field measurements[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(1): 40-56.

 

 

12.Damage

 

[1] Fischer P, Klassen M, Mergheim J, et al. Isogeometric analysis of 2D gradient elasticity[J]. Computational Mechanics. 2011, 47(3): 325-334.

 

[2] Verhoosel C V, Scott M A, Hughes T J, et al. An isogeometric analysis approach to gradient damage models[J]. International Journal for Numerical Methods in Engineering. 2011, 86(1): 115-134.

 

[3] Deng X, Korobenko A, Yan J, et al. Isogeometric analysis of continuum damage in rotation-free composite shells[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 349-372.

 

[4] Thai T Q, Rabczuk T, Bazilevs Y, et al. A higher-order stress-based gradient-enhanced damage model based on isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 304: 584-604.

 

[5] Zhang G, Khandelwal K. Modeling of nonlocal damage-plasticity in beams using isogeometric analysis[J]. Computers & Structures. 2016, 165: 76-95.

 

 

13.Dynamics

 

[1] Cottrell J A, Reali A, Bazilevs Y, et al. Isogeometric analysis of structural vibrations[J]. Computer methods in applied mechanics and engineering. 2006, 195(41): 5257-5296.

 

[2] Reali A. An isogeometric analysis approach for the study of structural vibrations[J]. Journal of Earthquake Engineering. 2006, 10(spec01): 1-30.

 

[3] Hughes T J, Reali A, Sangalli G. Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS[J]. Computer methods in applied mechanics and engineering. 2008, 197(49): 4104-4124.

 

[4] Willberg C, Duczek S, Perez J V, et al. Comparison of different higher order finite element schemes for the simulation of Lamb waves[J]. Computer methods in applied mechanics and engineering. 2012, 241: 246-261.

 

[5] Wang D, Liu W, Zhang H. Novel higher order mass matrices for isogeometric structural vibration analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 260: 92-108.

 

[6] Lee S J, Park K S. Vibrations of Timoshenko beams with isogeometric approach[J]. Applied Mathematical Modelling. 2013, 37(22): 9174-9190.

 

[7] Weeger O, Wever U, Simeon B. Nonlinear frequency response analysis of structural vibrations[J]. Computational Mechanics. 2014, 54(6): 1477-1495.

 

[8] Gao L, Calo V M. Fast isogeometric solvers for explicit dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 274: 19-41.

 

[9] Idesman A, Pham D, Foley J R, et al. Accurate solutions of wave propagation problems under impact loading by the standard, spectral and isogeometric high-order finite elements. Comparative study of accuracy of different space-discretization techniques[J]. Finite Elements in Analysis and Design. 2014, 88: 67-89.

 

[10] Idesman A. Accurate finite-element modeling of wave propagation in composite and functionally graded materials[J]. Composite Structures. 2014, 117: 298-308.

 

[11] Dedè L, Jäggli C, Quarteroni A. Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 320-348.

 

[12] Donatelli M, Garoni C, Manni C, et al. Spectral analysis and spectral symbol of matrices in isogeometric collocation methods[J]. Mathematics of Computation. 2015.

 

[13] Askari H, Esmailzadeh E, Barari A. A unified approach for nonlinear vibration analysis of curved structures using non-uniform rational B-spline representation[J]. Journal of Sound and Vibration. 2015, 353: 292-307.

 

[14] Hartmann S, Benson D J. Mass scaling and stable time step estimates for isogeometric analysis[J]. International Journal for Numerical Methods in Engineering. 2015, 102(3-4): 671-687.

 

[15] Wang D, Liu W, Zhang H. Superconvergent isogeometric free vibration analysis of Euler–Bernoulli beams and Kirchhoff plates with new higher order mass matrices[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 286: 230-267.

 

[16] Adam C, Bouabdallah S, Zarroug M, et al. Stable time step estimates for NURBS-based explicit dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 295: 581-605.

 

[17] Coox L, Deckers E, Vandepitte D, et al. A performance study of NURBS-based isogeometric analysis for interior two-dimensional time-harmonic acoustics[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

[18] Wang D, Liang Q, Zhang H. A superconvergent isogeometric formulation for eigenvalue computation of three dimensional wave equation[J]. Computational Mechanics. 2016: 1-24.

 

 

14.Electromagnetics

 

[1] Buffa A, Sangalli G, Vázquez R. Isogeometric analysis in electromagnetics: B-splines approximation[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(17): 1143-1152.

 

[2] Ratnani A, Sonnendrücker E. Isogeometric analysis in reduced magnetohydrodynamics[J]. Computational Science & Discovery. 2012, 5(1): 14007.

 

[3] Ratnani A, Sonnendrücker E. An arbitrary high-order spline finite element solver for the time domain maxwell equations[J]. Journal of Scientific Computing. 2012, 51(1): 87-106.

 

[4] 张勇, 林皋, 胡志强,等. 等几何分析方法求解静电场非齐次边值问题[J]. 电波科学学报. 2012(05): 997-1004.

 

[5] 张勇, 林皋, 刘俊, 等. 波导本征问题的等几何分析方法[J]. 应用力学学报. 2012, 29(2): 113-119.

 

[6] 张勇, 林皋, 刘俊, 等. 等几何分析法应用于偏心柱面静电场问题[J]. 电波科学学报. 2012(01): 177-183.

 

[7] Buffa A, Sangalli G, Vázquez R. Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations[J]. Journal of Computational Physics. 2014, 257: 1291-1320.

 

 

15.Fluid mechanics

 

[1] Bazilevs Y, Michler C, Calo V M, et al. Weak Dirichlet boundary conditions for wall-bounded turbulent flows[J]. Computer Methods in Applied Mechanics and Engineering. 2007, 196(49): 4853-4862.

 

[2] Bazilevs Y, Calo V M, Tezduyar T E, et al. YZβ discontinuity capturing for advection‐dominated processes with application to arterial drug delivery[J]. International Journal for Numerical Methods in Fluids. 2007, 54(6‐8): 593-608.

 

[3] Bazilevs Y, Hughes T J. Weak imposition of Dirichlet boundary conditions in fluid mechanics[J]. Computers & Fluids. 2007, 36(1): 12-26.

 

[4] Bazilevs Y, Hughes T. NURBS-based isogeometric analysis for the computation of flows about rotating components[J]. Computational Mechanics. 2008, 43(1): 143-150.

 

[5] Bazilevs Y, Akkerman I. Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual-based variational multiscale method[J]. Journal of Computational Physics. 2010, 229(9): 3402-3414.

 

[6] Bazilevs Y, Michler C, Calo V M, et al. Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(13): 780-790.

 

[7] Akkerman I, Bazilevs Y, Kees C E, et al. Isogeometric analysis of free-surface flow[J]. Journal of Computational Physics. 2011, 230(11): 4137-4152.

 

[8] Buffa A, De Falco C, Sangalli G. IsoGeometric Analysis: Stable elements for the 2D Stokes equation[J]. International Journal for Numerical Methods in Fluids. 2011, 65(11‐12): 1407-1422.

 

[9] Hsu M, Akkerman I, Bazilevs Y. High-performance computing of wind turbine aerodynamics using isogeometric analysis[J]. Computers & Fluids. 2011, 49(1): 93-100.

 

[10] Manni C, Pelosi F, Sampoli M L. Isogeometric analysis in advection–diffusion problems: Tension splines approximation[J]. Journal of Computational and Applied Mathematics. 2011, 236(4): 511-528.

 

[11] Nielsen P N, Gersborg A R, Gravesen J, et al. Discretizations in isogeometric analysis of Navier–Stokes flow[J]. Computer methods in applied mechanics and engineering. 2011, 200(45): 3242-3253.

 

[12] Takizawa K, Henicke B, Montes D, et al. Numerical-performance studies for the stabilized space–time computation of wind-turbine rotor aerodynamics[J]. Computational Mechanics. 2011, 48(6): 647-657.

 

[13] Takizawa K, Henicke B, Tezduyar T E, et al. Stabilized space–time computation of wind-turbine rotor aerodynamics[J]. Computational Mechanics. 2011, 48(3): 333-344.

 

[14] Chang K, Hughes T J R, Calo V M. Isogeometric variational multiscale large-eddy simulation of fully-developed turbulent flow over a wavy wall[J]. Computers & Fluids. 2012, 68: 94-104.

 

[15] Großmann D, Jüttler B, Schlusnus H, et al. Isogeometric simulation of turbine blades for aircraft engines[J]. Computer Aided Geometric Design. 2012, 29(7): 519-531.

 

[16] Speleers H, Manni C, Pelosi F, et al. Isogeometric analysis with Powell–Sabin splines for advection–diffusion–reaction problems[J]. Computer methods in applied mechanics and engineering. 2012, 221: 132-148.

 

[17] Stein P, Hsu M, Bazilevs Y, et al. Operator-and template-based modeling of solid geometry for Isogeometric Analysis with application to Vertical Axis Wind Turbine simulation[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 213: 71-83.

 

[18] 张勤, 万能, 莫蓉, et al. 二维线性对流扩散问题的 NURBS 等几何分析[J]. 计算机辅助设计与图形学学报. 2012, 24(4): 520-527.

 

[19] Bazilevs Y, Akkerman I, Benson D J, et al. Isogeometric analysis of lagrangian hydrodynamics[J]. Journal of Computational Physics. 2013, 243: 224-243.

 

[20] Evans J A, Hughes T J. Isogeometric divergence-conforming B-splines for the unsteady Navier-Stokes equations[J]. Journal of Computational Physics. 2013, 241: 141-167.

 

[21] Motlagh Y G, Ahn H T, Hughes T J, et al. Simulation of laminar and turbulent concentric pipe flows with the isogeometric variational multiscale method[J]. Computers & Fluids. 2013, 71: 146-155.

 

[22] Bazilevs Y, Long C C, Akkerman I, et al. Isogeometric analysis of Lagrangian hydrodynamics: Axisymmetric formulation in the rz-cylindrical coordinates[J]. Journal of Computational Physics. 2014, 262: 244-261.

 

[23] John V, Schumacher L. A study of isogeometric analysis for scalar convection–diffusion equations[J]. Applied Mathematics Letters. 2014, 27: 43-48.

 

[24] Tagliabue A, Dedè L, Quarteroni A. Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics[J]. Computers & Fluids. 2014, 102: 277-303.

 

[25] 陈德祥, 徐自力. 多重网格在黏性流动最小二乘等几何模拟中的应用[J]. 西安交通大学学报. 2014, 48(11): 122-127.

 

[26] 陈德祥, 刘帅, 徐自力, et al. 非稳态流动的隐式最小二乘等几何方法[J]. 计算力学学报. 2015, 32(5): 639-643.

 

[27] Amini R, Maghsoodi R, Moghaddam N Z. Simulating free surface problem using isogeometric analysis[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2016, 38(2): 413-421.

 

[28] Rasool R, Corbett C J, Sauer R A. A strategy to interface isogeometric analysis with Lagrangian finite elements—application to incompressible flow problems[J]. Computers & Fluids. 2016.

 

[29] Takizawa K, Tezduyar T E, Otoguro Y, et al. Turbocharger flow computations with the Space–Time Isogeometric Analysis (ST-IGA)[J]. Computers & Fluids. 2016.

 

 

16.Fluid-structure interaction

 

[1] Bazilevs Y, Calo V M, Zhang Y, et al. Isogeometric fluid–structure interaction analysis with applications to arterial blood flow[J]. Computational Mechanics. 2006, 38(4-5): 310-322.

 

[2] Bazilevs Y, Calo V M, Hughes T J, et al. Isogeometric fluid-structure interaction: theory, algorithms, and computations[J]. Computational mechanics. 2008, 43(1): 3-37.

 

[3] Bazilevs Y, Gohean J R, Hughes T, et al. Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device[J]. Computer Methods in Applied Mechanics and Engineering. 2009, 198(45): 3534-3550.

 

[4] Bazilevs Y, Hsu M C, Kiendl J, et al. 3D simulation of wind turbine rotors at full scale. Part II: Fluid–structure interaction modeling with composite blades[J]. International Journal for Numerical Methods in Fluids. 2011, 65(1‐3): 236-253.

 

[5] Bazilevs Y, Hsu M, Scott M A. Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 249: 28-41.

 

[6] Bazilevs Y, Hsu M C, Kiendl J, et al. A computational procedure for prebending of wind turbine blades[J]. International Journal for Numerical Methods in Engineering. 2012, 89(3): 323-336.

 

[7] Hsu M, Bazilevs Y. Fluid–structure interaction modeling of wind turbines: simulating the full machine[J]. Computational Mechanics. 2012, 50(6): 821-833.

 

[8] Bazilevs Y, Hsu M, Bement M T. Adjoint-based control of fluid-structure interaction for computational steering applications[J]. Procedia Computer Science. 2013, 18: 1989-1998.

 

[9] Korobenko A, Hsu M, Akkerman I, et al. Structural mechanics modeling and FSI simulation of wind turbines[J]. Mathematical Models and Methods in Applied Sciences. 2013, 23(02): 249-272.

 

[10] Long C C, Marsden A L, Bazilevs Y. Fluid–structure interaction simulation of pulsatile ventricular assist devices[J]. Computational Mechanics. 2013, 52(5): 971-981.

 

[11] Hsu M, Kamensky D, Bazilevs Y, et al. Fluid–structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation[J]. Computational mechanics. 2014, 54(4): 1055-1071.

 

[12] Bazilevs Y, Takizawa K, Tezduyar T E, et al. Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods[J]. Archives of Computational Methods in Engineering. 2014, 21(4): 359-398.

 

[13] Hsu M, Kamensky D, Xu F, et al. Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models[J]. Computational mechanics. 2015, 55(6): 1211-1225.

 

 

17.Masonry arches

 

[1] Cazzani A, Malagù M, Turco E. Isogeometric analysis: a powerful numerical tool for the elastic analysis of historical masonry arches[J]. Continuum Mechanics and Thermodynamics. 2016, 28(1-2): 139-156.

 

 

18.Plastic analysis

 

[1] Elguedj T, Bazilevs Y, Calo V M, et al. F-bar projection method for finite deformation elasticity and plasticity using nurbs based isogeometric analysis[J]. International Journal of Material Forming. 2008, 1: 1091-1094.

 

[2] Kalali A T, Hassani B, Hadidi-Moud S. Elastic-plastic analysis of pressure vessels and rotating disks made of functionally graded materials using the isogeometric approach[J]. Journal of Theoretical and Applied Mechanics. 2016, 54(1): 113-125.

 

 

19.Nearly incompressible materials

 

[1] Elguedj T, Bazilevs Y, Calo V M, et al. and projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements[J]. Computer methods in applied mechanics and engineering. 2008, 197(33): 2732-2762.

 

[2] Auricchio F, Da Veiga L B, Lovadina C, et al. The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(5): 314-323.

 

[3] Taylor R L. Isogeometric analysis of nearly incompressible solids[J]. International Journal for Numerical Methods in Engineering. 2011, 87(1‐5): 273-288.

 

[4] Mathisen K M, Okstad K M, Kvamsdal T, et al. Isogeometric analysis of finite deformation nearly incompressible solids[J]. Journal of Structural Mechanics. 2011, 44(3): 260-278.

 

[5] Cardoso R P, Cesar De Sa J. The enhanced assumed strain method for the isogeometric analysis of nearly incompressible deformation of solids[J]. International Journal for Numerical Methods in Engineering. 2012, 92(1): 56-78.

 

[6] Elguedj T, Hughes T J. Isogeometric analysis of nearly incompressible large strain plasticity[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 268: 388-416.

 

[7] Kadapa C, Dettmer W G, Perić D. Subdivision based mixed methods for isogeometric analysis of linear and nonlinear nearly incompressible materials[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

 

20.Porous medium

 

[1] Irzal F, Remmers J J, Verhoosel C V, et al. Isogeometric finite element analysis of poroelasticity[J]. International Journal for Numerical and Analytical Methods in Geomechanics. 2013, 37(12): 1891-1907.

 

[2] Gomez H, Cueto-Felgueroso L, Juanes R. Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium[J]. Journal of Computational Physics. 2013, 238: 217-239.

 

[3] Nguyen M N, Bui T Q, Yu T, et al. Isogeometric analysis for unsaturated flow problems[J]. Computers and Geotechnics. 2014, 62: 257-267.

 

[4] Vuong A, Ager C, Wall W A. Two finite element approaches for Darcy and Darcy-Brinkman flow through deformable porous media—Mixed method vs. NURBS based (isogeometric) continuity[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

 

21.Beams

 

[1] Nagy A P, Abdalla M M, Gürdal Z. Isogeometric sizing and shape optimisation of beam structures[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(17): 1216-1230.

 

[2] Bouclier R, Elguedj T, Combescure A. Locking free isogeometric formulations of curved thick beams[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 245: 144-162.

 

[3] Da Veiga L B, Lovadina C, Reali A. Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 241: 38-51.

 

[4] Dedè L, Santos H A F A. B-spline goal-oriented error estimators for geometrically nonlinear rods[J]. Computational Mechanics. 2012, 49(1): 35-52.

 

[5] Weeger O, Wever U, Simeon B. Isogeometric analysis of nonlinear Euler–Bernoulli beam vibrations[J]. Nonlinear Dynamics. 2013, 72(4): 813-835.

 

[6] Cazzani A, Malagù M, Turco E. Isogeometric analysis of plane-curved beams[J]. Mathematics and Mechanics of Solids. 2014: 1567007807.

 

[7] Lezgy-Nazargah M. An isogeometric approach for the analysis of composite steel–concrete beams[J]. Thin-Walled Structures. 2014, 84: 406-415.

 

[8] Askari H, Esmailzadeh E, Barari A. A unified approach for nonlinear vibration analysis of curved structures using non-uniform rational B-spline representation[J]. Journal of Sound and Vibration. 2015, 353: 292-307.

 

[9] Cazzani A, Malagù M, Turco E, et al. Constitutive models for strongly curved beams in the frame of isogeometric analysis[J]. Mathematics and Mechanics of Solids. 2015: 1565962029.

 

[10] Ghasemi H, Kerfriden P, Bordas S P A, et al. Interfacial shear stress optimization in sandwich beams with polymeric core using non-uniform distribution of reinforcing ingredients[J]. Composite Structures. 2015, 120: 221-230.

 

[11] Kiendl J, Auricchio F, Hughes T, et al. Single-variable formulations and isogeometric discretizations for shear deformable beams[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 988-1004.

 

[12] Lezgy-Nazargah M. Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach[J]. Aerospace Science and Technology. 2015, 45: 154-164.

 

[13] Luu A, Kim N, Lee J. NURBS-based isogeometric vibration analysis of generally laminated deep curved beams with variable curvature[J]. Composite Structures. 2015, 119: 150-165.

 

[14] Maurin F, Dedè L, Spadoni A. Isogeometric rotation-free analysis of planar extensible-elastica for static and dynamic applications[J]. Nonlinear Dynamics. 2015, 81(1-2): 77-96.

 

[15] Bauer A M, Breitenberger M, Philipp B, et al. Nonlinear isogeometric spatial Bernoulli beam[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 303: 101-127.

 

[16] Hosseini S F, Moetakef-Imani B, Hadidi-Moud S, et al. The effect of parameterization on isogeometric analysis of free-form curved beams[J]. Acta Mechanica. 2016: 1-16.

 

[17] Zhang G, Alberdi R, Khandelwal K. Analysis of three-dimensional curved beams using isogeometric approach[J]. Engineering Structures. 2016, 117: 560-574.

 

 

22.Plates

 

[1] Echter R, Bischoff M. Numerical efficiency, locking and unlocking of NURBS finite elements[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(5): 374-382.

 

[2] Shojaee S, Izadpanah E, Valizadeh N, et al. Free vibration analysis of thin plates by using a NURBS-based isogeometric approach[J]. Finite Elements in Analysis and Design. 2012, 61: 23-34.

 

[3] Thai C H, Nguyen Xuan H, Nguyen Thanh N, et al. Static, free vibration, and buckling analysis of laminated composite Reissner–Mindlin plates using NURBS‐based isogeometric approach[J]. International Journal for Numerical Methods in Engineering. 2012, 91(6): 571-603.

 

[4] Shojaee S, Valizadeh N, Izadpanah E, et al. Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method[J]. Composite Structures. 2012, 94(5): 1677-1693.

 

[5] Kapoor H, Kapania R K. Geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates[J]. Composite Structures. 2012, 94(12): 3434-3447.

 

[6] Da Veiga L B, Buffa A, Lovadina C, et al. An isogeometric method for the Reissner–Mindlin plate bending problem[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 209: 45-53.

 

[7] Thai C H, Ferreira A, Carrera E, et al. Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory[J]. Composite Structures. 2013, 104: 196-214.

 

[8] Tran L V, Ferreira A, Nguyen-Xuan H. Isogeometric analysis of functionally graded plates using higher-order shear deformation theory[J]. Composites Part B: Engineering. 2013, 51: 368-383.

 

[9] Yin S, Yu T, Liu P. Free vibration analyses of FGM thin plates by isogeometric analysis based on classical plate theory and physical neutral surface[J]. Advances in Mechanical Engineering. 2013, 5: 634584.

 

[10] Tran L V, Thai C H, Nguyen-Xuan H. An isogeometric finite element formulation for thermal buckling analysis of functionally graded plates[J]. Finite Elements in Analysis and Design. 2013, 73: 65-76.

 

[11] Dornisch W, Klinkel S, Simeon B. Isogeometric Reissner–Mindlin shell analysis with exactly calculated director vectors[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 253: 491-504.

 

[12] Nguyen-Xuan H, Thai C H, Nguyen-Thoi T. Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory[J]. Composites Part B: Engineering. 2013, 55: 558-574.

 

[13] Valizadeh N, Natarajan S, Gonzalez-Estrada O A, et al. NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter[J]. Composite Structures. 2013, 99: 309-326.

 

[14] Valizadeh N, Bui T Q, Vu V T, et al. Isogeometric simulation for buckling, free and forced vibration of orthotropic plates[J]. International Journal of Applied Mechanics. 2013, 5(02): 1350017.

 

[15] Kapoor H, Kapania R K, Soni S R. Interlaminar stress calculation in composite and sandwich plates in NURBS Isogeometric finite element analysis[J]. Composite Structures. 2013, 106: 537-548.

 

[16] Lee S, Cho S. Isogeometric Shape Design Sensitivity Analysis of Mindlin Plates[J]. Journal of the Computational Structural Engineering Institute of Korea. 2013, 26(4): 255-262.

 

[17] 尹硕辉, 余天堂, 刘鹏. 基于等几何有限元法的功能梯度板自由振动分析[J]. 振动与冲击. 2013, 32(24): 180-186.

 

[18] 李新康, 张继发, 郑耀. Mindlin 板的等几何分析[J]. 固体力学学报. 2013, 1.

 

[19] Thai C H, Ferreira A, Bordas S, et al. Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory[J]. European Journal of Mechanics-A/Solids. 2014, 43: 89-108.

 

[20] Guo Y, Nagy A P, Gürdal Z. A layerwise theory for laminated composites in the framework of isogeometric analysis[J]. Composite Structures. 2014, 107: 447-457.

 

[21] Nguyen-Xuan H, Tran L V, Thai C H, et al. Isogeometric analysis of functionally graded plates using a refined plate theory[J]. Composites Part B: Engineering. 2014, 64: 222-234.

 

[22] Le-Manh T, Lee J. Postbuckling of laminated composite plates using NURBS-based isogeometric analysis[J]. Composite Structures. 2014, 109: 286-293.

 

[23] Nguyen V P, Kerfriden P, Bordas S P. Two-and three-dimensional isogeometric cohesive elements for composite delamination analysis[J]. Composites Part B: Engineering. 2014, 60: 193-212.

 

[24] Yin S, Hale J S, Yu T, et al. Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates[J]. Composite Structures. 2014, 118: 121-138.

 

[25] Guo Y, Ruess M, Gürdal Z. A contact extended isogeometric layerwise approach for the buckling analysis of delaminated composites[J]. Composite Structures. 2014, 116: 55-66.

 

[26] Thai C H, Kulasegaram S, Tran L V, et al. Generalized shear deformation theory for functionally graded isotropic and sandwich plates based on isogeometric approach[J]. Computers & Structures. 2014, 141: 94-112.

 

[27] Tran L V, Thai C H, Le H T, et al. Isogeometric analysis of laminated composite plates based on a four-variable refined plate theory[J]. Engineering Analysis with Boundary Elements. 2014, 47: 68-81.

 

[28] Nguyen V, Nguyen T, Thai H, et al. A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates[J]. Composites Part B: Engineering. 2014, 66: 233-246.

 

[29] Thai C H, Nguyen-Xuan H, Bordas S, et al. Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory[J]. Mechanics of Advanced Materials and Structures. 2015, 22(6): 451-469.

 

[30] Yu T T, Yin S, Bui T Q, et al. A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates[J]. Finite Elements in Analysis and Design. 2015, 96: 1-10.

 

[31] Phung-Van P, Abdel-Wahab M, Liew K M, et al. Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory[J]. Composite Structures. 2015, 123: 137-149.

 

[32] Phung-Van P, De Lorenzis L, Thai C H, et al. Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements[J]. Computational Materials Science. 2015, 96: 495-505.

 

[33] Kapl M, Vitrih V, Jüttler B, et al. Isogeometric analysis with geometrically continuous functions on two-patch geometries[J]. Computers & Mathematics with Applications. 2015, 70(7): 1518-1538.

 

[34] Tran L V, Lee J, Nguyen-Van H, et al. Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory[J]. International Journal of Non-Linear Mechanics. 2015, 72: 42-52.

 

[35] Beirão Da Veiga L, Hughes T, Kiendl J, et al. A locking-free model for Reissner–Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS[J]. Mathematical Models and Methods in Applied Sciences. 2015, 25(08): 1519-1551.

 

[36] Jari H, Atri H R, Shojaee S. Nonlinear thermal analysis of functionally graded material plates using a NURBS based isogeometric approach[J]. Composite Structures. 2015, 119: 333-345.

 

[37] Tran L V, Ly H A, Lee J, et al. Vibration analysis of cracked FGM plates using higher-order shear deformation theory and extended isogeometric approach[J]. International Journal of Mechanical Sciences. 2015, 96: 65-78.

 

[38] Reali A, Gomez H. An isogeometric collocation approach for Bernoulli–Euler beams and Kirchhoff plates[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 623-636.

 

[39] Pandey S, Pradyumna S. Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory[J]. European Journal of Mechanics - A/Solids. 2015, 51: 55-66.

 

[40] Nguyen N, Hui D, Lee J, et al. An efficient computational approach for size-dependent analysis of functionally graded nanoplates[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 297: 191-218.

 

[41] Yu T, Yin S, Bui T Q, et al. NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method[J]. Thin-Walled Structures. 2016, 101: 141-156.

 

[42] Tran L V, Phung-Van P, Lee J, et al. Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates[J]. Composite Structures. 2016.

 

[43] Thai C H, Zenkour A M, Wahab M A, et al. A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis[J]. Composite Structures. 2016, 139: 77-95.

 

[44] Thai C H, Ferreira A, Wahab M A, et al. A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis[J]. Acta Mechanica. 2016: 1-26.

 

[45] Owens A R, Welch J A, Kópházi J, et al. Discontinuous isogeometric analysis methods for the first-order form of the neutron transport equation with discrete ordinate (S N) angular discretisation[J]. Journal of Computational Physics. 2016, 315: 501-535.

 

[46] Le-Manh T, Luu-Anh T, Lee J. Isogeometric analysis for flexural behavior of composite plates considering large deformation with small rotations[J]. Mechanics of Advanced Materials and Structures. 2016, 23(3): 328-336.

 

[47] Nguyen T N, Thai C H, Nguyen-Xuan H. On the general framework of high order shear deformation theories for laminated composite plate structures: A novel unified approach[J]. International Journal of Mechanical Sciences. 2016, 110: 242-255.

 

 

23.Shells

 

[1] Kiendl J, Bletzinger K, Linhard J, et al. Isogeometric shell analysis with Kirchhoff–Love elements[J]. Computer Methods in Applied Mechanics and Engineering. 2009, 198(49): 3902-3914.

 

[2] Uhm T K, Youn S K. T‐spline finite element method for the analysis of shell structures[J]. International Journal for Numerical Methods in Engineering. 2009, 80(4): 507-536.

 

[3] Kiendl J, Bazilevs Y, Hsu M, et al. The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(37): 2403-2416.

 

[4] Benson D J, Bazilevs Y, Hsu M, et al. Isogeometric shell analysis: the Reissner–Mindlin shell[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(5): 276-289.

 

[5] Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, et al. Rotation free isogeometric thin shell analysis using PHT-splines[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(47): 3410-3424.

 

[6] Benson D J, Bazilevs Y, Hsu M, et al. A large deformation, rotation-free, isogeometric shell[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(13): 1367-1378.

 

[7] Hosseini S, Remmers J J, Verhoosel C V, et al. An isogeometric solid‐like shell element for nonlinear analysis[J]. International Journal for Numerical Methods in Engineering. 2013, 95(3): 238-256.

 

[8] Thai C H, Rabczuk T, Nguyen-Xuan H. A rotation-free isogeometric analysis for composite sandwich thin plates[J]. International Journal of Composite Materials. 2013, 3(A): 10-18.

 

[9] Echter R, Oesterle B, Bischoff M. A hierarchic family of isogeometric shell finite elements[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 254: 170-180.

 

[10] Benson D J, Hartmann S, Bazilevs Y, et al. Blended isogeometric shells[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 255: 133-146.

 

[11] Goyal A, Dörfel M R, Simeon B, et al. Isogeometric shell discretizations for flexible multibody dynamics[J]. Multibody System Dynamics. 2013, 30(2): 139-151.

 

[12] Nagy A P, Ijsselmuiden S T, Abdalla M M. Isogeometric design of anisotropic shells: optimal form and material distribution[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 264: 145-162.

 

[13] Casanova C F, Gallego A. NURBS-based analysis of higher-order composite shells[J]. Composite Structures. 2013, 104: 125-133.

 

[14] Bouclier R, Elguedj T, Combescure A. Efficient isogeometric NURBS-based solid-shell elements: Mixed formulation and-method[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 267: 86-110.

 

[15] Raknes S B, Deng X, Bazilevs Y, et al. Isogeometric rotation-free bending-stabilized cables: Statics, dynamics, bending strips and coupling with shells[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 263: 127-143.

 

[16] Dornisch W, Klinkel S, Simeon B. Isogeometric Reissner–Mindlin shell analysis with exactly calculated director vectors[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 253: 491-504.

 

[17] Bouclier R, Elguedj T, Combescure A. On the development of NURBS-based isogeometric solid shell elements: 2D problems and preliminary extension to 3D[J]. Computational Mechanics. 2013, 52(5): 1085-1112.

 

[18] Cocchetti G, Pagani M, Perego U. Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements[J]. Computers & Structures. 2013, 127: 39-52.

 

[19] Lu J, Zheng C. Dynamic cloth simulation by isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 268: 475-493.

 

[20] Hosseini S, Remmers J J, Verhoosel C V, et al. An isogeometric continuum shell element for non-linear analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 271: 1-22.

 

[21] Kiendl J, Schmidt R, Wüchner R, et al. Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 274: 148-167.

 

[22] Caseiro J F, Valente R, Reali A, et al. On the Assumed Natural Strain method to alleviate locking in solid-shell NURBS-based finite elements[J]. Computational Mechanics. 2014, 53(6): 1341-1353.

 

[23] Chen L, Nguyen-Thanh N, Nguyen-Xuan H, et al. Explicit finite deformation analysis of isogeometric membranes[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 277: 104-130.

 

[24] Amiri F, Millán D, Shen Y, et al. Phase-field modeling of fracture in linear thin shells[J]. Theoretical and Applied Fracture Mechanics. 2014, 69: 102-109.

 

[25] Sauer R A, Duong T X, Corbett C J. A computational formulation for constrained solid and liquid membranes considering isogeometric finite elements[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 271: 48-68.

 

[26] Dornisch W, Klinkel S. Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 276: 35-66.

 

[27] Greco L, Cuomo M. An implicit multi patch B-spline interpolation for Kirchhoff–Love space rod[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 269: 173-197.

 

[28] 张升刚, 王彦伟, 黄正东. 等几何壳体分析与形状优化[J]. 计算力学学报. 2014, 31(1): 115-119.

 

[29] Nguyen-Thanh N, Valizadeh N, Nguyen M N, et al. An extended isogeometric thin shell analysis based on Kirchhoff–Love theory[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 265-291.

 

[30] Deng X, Korobenko A, Yan J, et al. Isogeometric analysis of continuum damage in rotation-free composite shells[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 349-372.

 

[31] Kang P, Youn S. Isogeometric analysis of topologically complex shell structures[J]. Finite Elements in Analysis and Design. 2015, 99: 68-81.

 

[32] Breitenberger M, Apostolatos A, Philipp B, et al. Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 401-457.

 

[33] Caseiro J F, Valente R, Reali A, et al. Assumed Natural Strain NURBS-based solid-shell element for the analysis of large deformation elasto-plastic thin-shell structures[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 861-880.

 

[34] Kiendl J, Hsu M, Wu M C, et al. Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 291: 280-303.

 

[35] Tepole A B, Kabaria H, Bletzinger K, et al. Isogeometric Kirchhoff–Love shell formulations for biological membranes[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 293: 328-347.

 

[36] Guo Y, Ruess M. Nitsche’s method for a coupling of isogeometric thin shells and blended shell structures[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 881-905.

 

[37] Zhang X, Jin C, Hu P, et al. NURBS modeling and isogeometric shell analysis for complex tubular engineering structures[J]. Computational and Applied Mathematics. 2016: 1-21.

 

[38] Riffnaller-Schiefer A, Augsdörfer U H, Fellner D W. Isogeometric shell analysis with NURBS compatible subdivision surfaces[J]. Applied Mathematics and Computation. 2016, 272: 139-147.

 

[39] Greco L, Cuomo M. An isogeometric implicit G1 mixed finite element for Kirchhoff space rods[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 298: 325-349.

 

[40] Dornisch W, Müller R, Klinkel S. An efficient and robust rotational formulation for isogeometric Reissner–Mindlin shell elements[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 303: 1-34.

 

[41] Ambati M, De Lorenzis L. Phase-field modeling of brittle and ductile fracture in shells with isogeometric NURBS-based solid-shell elements[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

 

24.Material optimization

 

[1] Nagy A P, Ijsselmuiden S T, Abdalla M M. Isogeometric design of anisotropic shells: optimal form and material distribution[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 264: 145-162.

 

[2] Le-Manh T, Lee J. Stacking sequence optimization for maximum strengths of laminated composite plates using genetic algorithm and isogeometric analysis[J]. Composite Structures. 2014, 116: 357-363.

 

[3] Blanchard L, Duvigneau R, Vuong A, et al. Shape Gradient for Isogeometric Structural Design[J]. Journal of Optimization Theory and Applications. 2014, 161(2): 361-367.

 

[4] Taheri A H, Hassani B, Moghaddam N Z. Thermo-elastic optimization of material distribution of functionally graded structures by an isogeometrical approach[J]. International Journal of Solids and Structures. 2014, 51(2): 416-429.

 

[5] Herath M T, Natarajan S, Prusty B G, et al. Isogeometric analysis and Genetic Algorithm for shape-adaptive composite marine propellers[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 835-860.

 

 

25.Shape optimization

 

[1] Wall W A, Frenzel M A, Cyron C. Isogeometric structural shape optimization[J]. Computer methods in applied mechanics and engineering. 2008, 197(33): 2976-2988.

 

[2] Cho S, Ha S. Isogeometric shape design optimization: exact geometry and enhanced sensitivity[J]. Structural and Multidisciplinary Optimization. 2009, 38(1): 53-70.

 

[3] Seo Y, Kim H, Youn S. Shape optimization and its extension to topological design based on isogeometric analysis[J]. International Journal of Solids and Structures. 2010, 47(11): 1618-1640.

 

[4] Ha S, Choi K K, Cho S. Numerical method for shape optimization using T-spline based isogeometric method[J]. Structural and Multidisciplinary Optimization. 2010, 42(3): 417-428.

 

[5] Qian X. Full analytical sensitivities in NURBS based isogeometric shape optimization[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(29): 2059-2071.

 

[6] Nagy A P, Abdalla M M, Gürdal Z. On the variational formulation of stress constraints in isogeometric design[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(41): 2687-2696.

 

[7] Nagy A P, Abdalla M M, Gürdal Z. Isogeometric sizing and shape optimisation of beam structures[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(17): 1216-1230.

 

[8] Li K, Qian X. Isogeometric analysis and shape optimization via boundary integral[J]. Computer-Aided Design. 2011, 43(11): 1427-1437.

 

[9] Hassani B, Tavakkoli S M, Moghadam N Z. Application of isogeometric analysis in structural shape optimization[J]. Scientia Iranica. 2011, 18(4): 846-852.

 

[10] Manh N D, Evgrafov A, Gersborg A R, et al. Isogeometric shape optimization of vibrating membranes[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(13): 1343-1353.

 

[11] Qian X, Sigmund O. Isogeometric shape optimization of photonic crystals via Coons patches[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(25): 2237-2255.

 

[12] Nagy A P, Abdalla M M, Gürdal Z. Isogeometric design of elastic arches for maximum fundamental frequency[J]. Structural and Multidisciplinary Optimization. 2011, 43(1): 135-149.

 

[13] Espath L F R, Linn R V, Awruch A M. Shape optimization of shell structures based on NURBS description using automatic differentiation[J]. International Journal for Numerical Methods in Engineering. 2011, 88(7): 613-636.

 

[14] Nguyen D M, Evgrafov A, Gravesen J. Isogeometric shape optimization for electromagnetic scattering problems[J]. Progress in Electromagnetics Research B. 2012, 45: 117-146.

 

[15] Koo B, Yoon M, Cho S. Isogeometric shape design sensitivity analysis using transformed basis functions for Kronecker delta property[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 253: 505-516.

 

[16] Park B, Seo Y, Sigmund O, et al. Shape optimization of the stokes flow problem based on isogeometric analysis[J]. Structural and Multidisciplinary Optimization. 2013, 48(5): 965-977.

 

[17] Yoon M, Ha S, Cho S. Isogeometric shape design optimization of heat conduction problems[J]. International Journal of Heat and Mass Transfer. 2013, 62: 272-285.

 

[18] Azegami H, Fukumoto S, Aoyama T. Shape optimization of continua using NURBS as basis functions[J]. Structural and Multidisciplinary Optimization. 2013, 47(2): 247-258.

 

[19] Nørtoft P, Gravesen J. Isogeometric shape optimization in fluid mechanics[J]. Structural and Multidisciplinary Optimization. 2013, 48(5): 909-925.

 

[20] Koo B, Ha S, Kim H, et al. Isogeometric Shape Design Optimization of Geometrically Nonlinear Structures[J]. Mechanics Based Design of Structures and Machines. 2013, 41(3): 337-358.

 

[21] Lee S, Cho S. Isogeometric Shape Design Sensitivity Analysis of Mindlin Plates[J]. Journal of the Computational Structural Engineering Institute of Korea. 2013, 26(4): 255-262.

 

[22] Park B, Seo Y, Sigmund O, et al. Shape optimization of the stokes flow problem based on isogeometric analysis[J]. Structural and Multidisciplinary Optimization. 2013, 48(5): 965-977.

 

[23] 李杨, 张卫红, 蔡守宇. 一种等几何形状优化的网格更新方法[J]. 机械制造. 2013, 51(4): 16-19.

 

[24] Blanchard L, Duvigneau R, Vuong A, et al. Shape gradient for isogeometric structural design[J]. Journal of Optimization Theory and Applications. 2014, 161(2): 361-367.

 

[25] Kiendl J, Schmidt R, Wüchner R, et al. Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 274: 148-167.

 

[26] Choi M, Cho S. Isogeometric shape design sensitivity analysis of stress intensity factors for curved crack problems[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 279: 469-496.

 

[27] Cai S, Zhang W, Zhu J, et al. Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 278: 361-387.

 

[28] 王辉明, 赵文. 基于等几何分析的结构形状优化设计研究[J]. 制造业自动化. 2014(03): 87-91.

 

[29] 张升刚, 王彦伟, 黄正东. 等几何壳体分析与形状优化[J]. 计算力学学报. 2014(01): 115-119.

 

[30] Fußeder D, Simeon B, Vuong A. Fundamental aspects of shape optimization in the context of isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 286: 313-331.

 

[31] Kostas K V, Ginnis A I, Politis C G, et al. Ship-hull shape optimization with a T-spline based BEM–isogeometric solver[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 611-622.

 

[32] Herath M T, Natarajan S, Prusty B G, et al. Isogeometric analysis and Genetic Algorithm for shape-adaptive composite marine propellers[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 835-860.

 

[33] Lee S, Cho S. Isogeometric configuration design optimization of built-up structures[J]. Structural and Multidisciplinary Optimization. 2015, 51(2): 319-331.

 

[34] Yoon M, Choi M, Cho S. Isogeometric configuration design optimization of heat conduction problems using boundary integral equation[J]. International Journal of Heat and Mass Transfer. 2015, 89: 937-949.

 

[35] 傅晓锦, 龙凯, 周利明, et al. 基于等几何裁剪分析的拓扑与形状集成优化[J]. 振动与冲击. 2015, 34(7): 162-173.

 

[36] Ding C S, Cui X Y, Li G Y. Accurate analysis and thickness optimization of tailor rolled blanks based on isogeometric analysis[J]. Structural and Multidisciplinary Optimization. 2016: 1-17.

 

[37] Alic V, Persson K. Form finding with dynamic relaxation and isogeometric membrane elements[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 300: 734-747.

 

[38] Gillebaart E, De Breuker R. Low-fidelity 2D isogeometric aeroelastic analysis and optimization method with application to a morphing airfoil[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

 

26.Topology optimization

 

[1] Seo Y, Kim H, Youn S. Isogeometric topology optimization using trimmed spline surfaces[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(49): 3270-3296.

 

[2] Seo Y, Kim H, Youn S. Shape optimization and its extension to topological design based on isogeometric analysis[J]. International Journal of Solids and Structures. 2010, 47(11-12): 1618-1640.

 

[3] Dedè L, Borden M J, Hughes T J. Isogeometric analysis for topology optimization with a phase field model[J]. Archives of Computational Methods in Engineering. 2012, 19(3): 427-465.

 

[4] Hassani B, Khanzadi M, Tavakkoli S M. An isogeometrical approach to structural topology optimization by optimality criteria[J]. Structural and multidisciplinary optimization. 2012, 45(2): 223-233.

 

[5] Qian X. Topology optimization in B-spline space[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 265: 15-35.

 

[6] Wang Y, Benson D J. Isogeometric analysis for parameterized LSM-based structural topology optimization[J]. Computational Mechanics. 2016, 57(1): 19-35.

 

[7] Kazemi H S, Tavakkoli S M, Naderi R. Isogeometric topology optimization of structures considering weight minimization and local stress constraints[J]. Int J Optim Civil Eng. 2016, 6(2): 303-317.

 

 

27.Phase field

 

[1] Gómez H, Calo V M, Bazilevs Y, et al. Isogeometric analysis of the Cahn–Hilliard phase-field model[J]. Computer methods in applied mechanics and engineering. 2008, 197(49): 4333-4352.

 

[2] Gomez H, Hughes T J, Nogueira X, et al. Isogeometric analysis of the isothermal Navier–Stokes–Korteweg equations[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(25): 1828-1840.

 

[3] Dedè L, Borden M J, Hughes T J. Isogeometric analysis for topology optimization with a phase field model[J]. Archives of Computational Methods in Engineering. 2012, 19(3): 427-465.

 

[4] Gomez H, Nogueira X. An unconditionally energy-stable method for the phase field crystal equation[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 249: 52-61.

 

[5] Borden M J, Verhoosel C V, Scott M A, et al. A phase-field description of dynamic brittle fracture[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 217: 77-95.

 

[6] Liu J, Dedè L, Evans J A, et al. Isogeometric analysis of the advective Cahn–Hilliard equation: spinodal decomposition under shear flow[J]. Journal of Computational Physics. 2013, 242: 321-350.

 

[7] Vilanova G, Colominas I, Gomez H. Capillary networks in tumor angiogenesis: From discrete endothelial cells to phase‐field averaged descriptions via isogeometric analysis[J]. International journal for numerical methods in biomedical engineering. 2013, 29(10): 1015-1037.

 

[8] Dhote R, Gomez H, Melnik R, et al. Isogeometric analysis of coupled thermo-mechanical phase-field models for shape memory alloys using distributed computing[J]. Procedia Computer Science. 2013, 18: 1068-1076.

 

[9] Vignal P A, Collier N, Calo V M. Phase field modeling using PetIGA[J]. Procedia Computer Science. 2013, 18: 1614-1623.

 

[10] Borden M J, Hughes T J, Landis C M, et al. A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 273: 100-118.

 

[11] Dhote R P, Gomez H, Melnik R, et al. Isogeometric analysis of a dynamic thermo-mechanical phase-field model applied to shape memory alloys[J]. Computational Mechanics. 2014, 53(6): 1235-1250.

 

[12] Gomez H, Reali A, Sangalli G. Accurate, efficient, and (iso) geometrically flexible collocation methods for phase-field models[J]. Journal of Computational Physics. 2014, 262: 153-171.

 

[13] Amiri F, Millán D, Shen Y, et al. Phase-field modeling of fracture in linear thin shells[J]. Theoretical and Applied Fracture Mechanics. 2014, 69: 102-109.

 

[14] Bartezzaghi A, Dedè L, Quarteroni A. Isogeometric analysis of high order partial differential equations on surfaces[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 295: 446-469.

 

[15] Dhote R P, Gomez H, Melnik R, et al. 3D coupled thermo-mechanical phase-field modeling of shape memory alloy dynamics via isogeometric analysis[J]. Computers & Structures. 2015, 154: 48-58.

 

[16] Kästner M, Metsch P, De Borst R. Isogeometric analysis of the Cahn–Hilliard equation–a convergence study[J]. Journal of Computational Physics. 2016, 305: 360-371.

 

[17] Hesch C, Schuß S, Dittmann M, et al. Isogeometric analysis and hierarchical refinement for higher-order phase-field models[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 303: 185-207.

 

[18] Bueno J, Starodumov I, Gomez H, et al. Three dimensional structures predicted by the modified phase field crystal equation[J]. Computational Materials Science. 2016, 111: 310-312.

 

[19] Hesch C, Schuß S, Dittmann M, et al. Isogeometric analysis and hierarchical refinement for higher-order phase-field models[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 303: 185-207.

 

[20] Heschv C, Franke M, Dittmann M, et al. Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

[21] Amiri F, Millán D, Arroyo M, et al. Fourth order phase-field model for local max-ent approximants applied to crack propagation[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

[22] Ambati M, De Lorenzis L. Phase-field modeling of brittle and ductile fracture in shells with isogeometric NURBS-based solid-shell elements[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

[23] Ambati M, Kruse R, De Lorenzis L. A phase-field model for ductile fracture at finite strains and its experimental verification[J]. Computational Mechanics. 2016, 57(1): 149-167.

 

 

28.IGA-BEM

 

[1] Li K, Qian X. Isogeometric analysis and shape optimization via boundary integral[J]. Computer-Aided Design. 2011, 43(11): 1427-1437.

 

[2] Gu J, Zhang J, Sheng X, et al. B-spline approximation in boundary face method for three-dimensional linear elasticity[J]. Engineering Analysis with Boundary Elements. 2011, 35(11): 1159-1167.

 

[3] Gu J, Zhang J, Li G. Isogeometric analysis in BIE for 3-D potential problem[J]. Engineering Analysis with Boundary Elements. 2012, 36(5): 858-865.

 

[4] Simpson R N, Bordas S P, Trevelyan J, et al. A two-dimensional isogeometric boundary element method for elastostatic analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 209: 87-100.

 

[5] Takahashi T, Matsumoto T. An application of fast multipole method to isogeometric boundary element method for Laplace equation in two dimensions[J]. Engineering Analysis with Boundary Elements. 2012, 36(12): 1766-1775.

 

[6] Gu J, Zhang J, Sheng X. The boundary face method with variable approximation by b-spline basis function[J]. International Journal of Computational Methods. 2012, 9(01): 1240009.

 

[7] 张勇, 林皋, 胡志强, et al. 基于等几何分析的比例边界有限元方法[J]. 计算力学学报. 2012(03): 433-438.

 

[8] Simpson R N, Bordas S P A, Lian H, et al. An isogeometric boundary element method for elastostatic analysis: 2D implementation aspects[J]. Computers & Structures. 2013, 118: 2-12.

 

[9] Scott M A, Simpson R N, Evans J A, et al. Isogeometric boundary element analysis using unstructured T-splines[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 254: 197-221.

 

[10] Peake M J, Trevelyan J, Coates G. Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 259: 93-102.

 

[11] Belibassakis K A, Gerostathis T P, Kostas K V, et al. A BEM-isogeometric method for the ship wave-resistance problem[J]. Ocean Engineering. 2013, 60: 53-67.

 

[12] Ginnis A I, Kostas K V, Politis C G, et al. Isogeometric boundary-element analysis for the wave-resistance problem using T-splines[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 279: 425-439.

 

[13] Lin G, Zhang Y, Hu Z, et al. Scaled boundary isogeometric analysis for 2D elastostatics[J]. Science China Physics, Mechanics and Astronomy. 2014, 57(2): 286-300.

 

[14] Simpson R N, Scott M A, Taus M, et al. Acoustic isogeometric boundary element analysis[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 269: 265-290.

 

[15] Heltai L, Arroyo M, Desimone A. Nonsingular isogeometric boundary element method for Stokes flows in 3D[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 268: 514-539.

 

[16] Marussig B, Beer G, Duenser C. Isogeometric boundary element method for the simulation in tunneling.[J]. Applied Mechanics & Materials. 2014(553).

 

[17] May S, Kästner M, Müller S, et al. A hybrid IGAFEM/IGABEM formulation for two-dimensional stationary magnetic and magneto-mechanical field problems[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 273: 161-180.

 

[18] Natarajan S, Wang J, Song C, et al. Isogeometric analysis enhanced by the scaled boundary finite element method[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 283: 733-762.

 

[19] Kostas K V, Ginnis A I, Politis C G, et al. Ship-hull shape optimization with a T-spline based BEM–isogeometric solver[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 611-622.

 

[20] Marussig B, Zechner J, Beer G, et al. Fast isogeometric boundary element method based on independent field approximation[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 458-488.

 

[21] Wang Y J, Benson D J. Multi-patch nonsingular isogeometric boundary element analysis in 3D[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 293: 71-91.

 

[22] Yoon M, Choi M, Cho S. Isogeometric configuration design optimization of heat conduction problems using boundary integral equation[J]. International Journal of Heat and Mass Transfer. 2015, 89: 937-949.

 

[23] Wang Y, Benson D J, Nagy A P. A multi-patch nonsingular isogeometric boundary element method using trimmed elements[J]. Computational Mechanics. 2015, 56(1): 173-191.

 

[24] Nguyen B H, Tran H D, Anitescu C, et al. An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

[25] Yoon M, Cho S. Isogeometric shape design sensitivity analysis of elasticity problems using boundary integral equations[J]. Engineering Analysis with Boundary Elements. 2016, 66: 119-128.

 

[26] Chen L, Simeon B, Klinkel S. A NURBS based Galerkin approach for the analysis of solids in boundary representation[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

[27] Aimi A, Diligenti M, Sampoli M L, et al. Isogemetric analysis and symmetric Galerkin BEM: A 2D numerical study[J]. Applied Mathematics and Computation. 2016, 272: 173-186.

 

[28] Feischl M, Gantner G, Haberl A, et al. Adaptive 2D IGA boundary element methods[J]. Engineering Analysis with Boundary Elements. 2016, 62: 141-153.

 

[29] Simpson R N, Liu Z. Acceleration of isogeometric boundary element analysis through a black-box fast multipole method[J]. Engineering Analysis with Boundary Elements. 2016, 66: 168-182.

 

 

29.IGA-collocation

 

[1] Auricchio F, Da Veiga L B, Hughes T, et al. Isogeometric collocation methods[J]. Mathematical Models and Methods in Applied Sciences. 2010, 20(11): 2075-2107.

 

[2] Da Veiga L B, Lovadina C, Reali A. Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 241: 38-51.

 

[3] Auricchio F, Da Veiga L B, Hughes T, et al. Isogeometric collocation for elastostatics and explicit dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 249: 2-14.

 

[4] Schillinger D, Evans J A, Reali A, et al. Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 267: 170-232.

 

[5] Auricchio F, Da Veiga L B, Kiendl J, et al. Locking-free isogeometric collocation methods for spatial Timoshenko rods[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 263: 113-126.

 

[6] Lin H, Hu Q, Xiong Y. Consistency and convergence properties of the isogeometric collocation method[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 267: 471-486.

 

[7] Gomez H, Reali A, Sangalli G. Accurate, efficient, and (iso) geometrically flexible collocation methods for phase-field models[J]. Journal of Computational Physics. 2014, 262: 153-171.

 

[8] Reali A, Gomez H. An isogeometric collocation approach for Bernoulli–Euler beams and Kirchhoff plates[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 623-636.

 

[9] Kiendl J, Auricchio F, Da Veiga L B, et al. Isogeometric collocation methods for the Reissner–Mindlin plate problem[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 489-507.

 

[10] De Lorenzis L, Evans J A, Hughes T, et al. Isogeometric collocation: Neumann boundary conditions and contact[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 21-54.

 

[11] Donatelli M, Garoni C, Manni C, et al. Spectral analysis and spectral symbol of matrices in isogeometric collocation methods[J]. Mathematics of Computation. 2015.

 

[12] Donatelli M, Garoni C, Manni C, et al. Robust and optimal multi-iterative techniques for IgA collocation linear systems[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 1120-1146.

 

[13] Manni C, Reali A, Speleers H. Isogeometric collocation methods with generalized B-splines[J]. Computers & Mathematics with Applications. 2015, 70(7): 1659-1675.

 

[14] Klinkel S, Chen L, Dornisch W. A NURBS based hybrid collocation–Galerkin method for the analysis of boundary represented solids[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 689-711.

 

[15] Anitescu C, Jia Y, Zhang Y J, et al. An isogeometric collocation method using superconvergent points[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 1073-1097.

 

[16] Schillinger D, Borden M J, Stolarski H K. Isogeometric collocation for phase-field fracture models[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 284: 583-610.

 

[17] Casquero H, Liu L, Zhang Y, et al. Isogeometric collocation using analysis-suitable T-splines of arbitrary degree[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 301: 164-186.

 

 

30.IGA-FCM(Finite cell method)

 

[1] Rank E, Kollmannsberger S, Sorger C, et al. Shell finite cell method: a high order fictitious domain approach for thin-walled structures[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(45): 3200-3209.

 

[2] Schillinger D, Rank E. An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(47-48): 3358-3380.

 

[3] Rank E, Ruess M, Kollmannsberger S, et al. Geometric modeling, isogeometric analysis and the finite cell method[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 249: 104-115.

 

[4] Schillinger D, Dede L, Scott M A, et al. An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 249: 116-150.

 

[5] Schillinger D, Ruess M, Zander N, et al. Small and large deformation analysis with the p-and B-spline versions of the finite cell method[J]. Computational Mechanics. 2012, 50(4): 445-478.

 

[6] Ruess M, Schillinger D, Bazilevs Y, et al. Weakly enforced essential boundary conditions for NURBS‐embedded and trimmed NURBS geometries on the basis of the finite cell method[J]. International Journal for Numerical Methods in Engineering. 2013, 95(10): 811-846.

 

[7] Schillinger D, Ruess M. The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models[J]. Archives of Computational Methods in Engineering. 2015, 22(3): 391-455.

 

[8] Zhang W, Zhao L, Cai S. Shape optimization of Dirichlet boundaries based on weighted B-spline finite cell method and level-set function[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 294: 359-383.

 

[9] Varduhn V, Hsu M C, Ruess M, et al. The tetrahedral finite cell method: higher‐order immersogeometric analysis on adaptive non‐boundary‐fitted meshes[J]. International Journal for Numerical Methods in Engineering. 2016.

 

[10] Tonon P, Carrazedo R, Sanches R A. Immersed normalized B-spline finite elements–A convergence study for 2D problems[J]. Finite Elements in Analysis and Design. 2016, 114: 57-67.

 

[11] Bandara K, Rüberg T, Cirak F. Shape optimisation with multiresolution subdivision surfaces and immersed finite elements[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 300: 510-539.

 

 

31.IGA-meshfree

 

[1] González D, Cueto E, Doblaré M. Higher‐order natural element methods: Towards an isogeometric meshless method[J]. International journal for numerical methods in engineering. 2008, 74(13): 1928-1954.

 

[2] Kim H, Youn S. Spline-based meshfree method[J]. International Journal for Numerical Methods in Engineering. 2012, 92(9): 802-834.

 

[3] Rosolen A, Arroyo M. Blending isogeometric analysis and local maximum entropy meshfree approximants[J]. Computer Methods in Applied Mechanics and Engineering. 2013, 264: 95-107.

 

[4] Lei Y, Chen Z, Yi T, et al. Isogeometric-meshfree coupled analysis of Kirchhoff plates[J]. Advances in Structural Engineering. 2014, 17(8): 1159-1176.

 

[5] Cardoso R P, de Sa J C. Blending moving least squares techniques with NURBS basis functions for nonlinear isogeometric analysis[J]. Computational Mechanics. 2014, 53(6): 1327-1340.

 

[6] Wang D, Zhang H. A consistently coupled isogeometric–meshfree method[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 268: 843-870.

 

[7] Moosavi M R, Khelil A. Isogeometric meshless finite volume method in nonlinear elasticity[J]. Acta Mechanica. 2015, 226(1): 123-135.

 

[8] Valizadeh N, Bazilevs Y, Chen J S, et al. A coupled IGA–Meshfree discretization of arbitrary order of accuracy and without global geometry parameterization[J]. Computer Methods in Applied Mechanics and Engineering. 2015, 293: 20-37.

 

 

32.Others

 

[1] Hughes T J, Cottrell J A, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement[J]. Computer methods in applied mechanics and engineering. 2005, 194(39): 4135-4195.

 

[2] Auricchio F, Da Veiga L B, Buffa A, et al. A fully “locking-free” isogeometric approach for plane linear elasticity problems: a stream function formulation[J]. Computer methods in applied mechanics and engineering. 2007, 197(1): 160-172.

 

[3] Lu J. Circular element: Isogeometric elements of smooth boundary[J]. Computer methods in applied mechanics and engineering. 2009, 198(30): 2391-2402.

 

[4] Lipton S, Evans J A, Bazilevs Y, et al. Robustness of isogeometric structural discretizations under severe mesh distortion[J]. Computer Methods in Applied Mechanics and Engineering. 2010, 199(5): 357-373.

 

[5] Schmidt R, Kiendl J, Bletzinger K, et al. Realization of an integrated structural design process: analysis-suitable geometric modelling and isogeometric analysis[J]. Computing and Visualization in Science. 2010, 13(7): 315-330.

 

[6] Fischer P, Klassen M, Mergheim J, et al. Isogeometric analysis of 2D gradient elasticity[J]. Computational Mechanics. 2011, 47(3): 325-334.

 

[7] Lu J, Zhou X. Cylindrical element: Isogeometric model of continuum rod[J]. Computer Methods in Applied Mechanics and Engineering. 2011, 200(1): 233-241.

 

[8] Kleiss S K, Jüttler B, Zulehner W. Enhancing isogeometric analysis by a finite element-based local refinement strategy[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 213: 168-182.

 

[9] Anders D, Weinberg K, Reichardt R. Isogeometric analysis of thermal diffusion in binary blends[J]. Computational Materials Science. 2012, 52(1): 182-188.

 

[10] Crouseilles N, Ratnani A, Sonnendrücker E. An isogeometric analysis approach for the study of the gyrokinetic quasi-neutrality equation[J]. Journal of Computational Physics. 2012, 231(2): 373-393.

 

[11] Hall S K, Eaton M D, Williams M. The application of isogeometric analysis to the neutron diffusion equation for a pincell problem with an analytic benchmark[J]. Annals of Nuclear Energy. 2012, 49: 160-169.

 

[12] Willberg C, Gabbert U. Development of a three-dimensional piezoelectric isogeometric finite element for smart structure applications[J]. Acta Mechanica. 2012, 223(8): 1837-1850.

 

[13] Gomez H, Nogueira X. A new space–time discretization for the Swift–Hohenberg equation that strictly respects the Lyapunov functional[J]. Communications in Nonlinear Science and Numerical Simulation. 2012, 17(12): 4930-4946.

 

[14] Masud A, Kannan R. B-splines and NURBS based finite element methods for Kohn–Sham equations[J]. Computer Methods in Applied Mechanics and Engineering. 2012, 241-244: 112-127.

 

[15] Nguyen V, Kerfriden P, Bordas S, et al. An integrated design-analysis framework for three dimensional composite panels[J]. Computer-Aided Design. 2013.

 

[16] Hassani B, Taheri A H, Moghaddam N Z. An improved isogeometrical analysis approach to functionally graded plane elasticity problems[J]. Applied Mathematical Modelling. 2013, 37(22): 9242-9268.

 

[17] Jaxon N, Qian X. Isogeometric analysis on triangulations[J]. Computer-Aided Design. 2014, 46: 45-57.

 

[18] Stein P, Xu B. 3D Isogeometric Analysis of intercalation-induced stresses in Li-ion battery electrode particles[J]. Computer Methods in Applied Mechanics and Engineering. 2014, 268: 225-244.

 

[19] Zhang F, Xu Y, Chen F. Discontinuous galerkin methods for isogeometric analysis for elliptic equations on surfaces[J]. Communications in Mathematics and Statistics. 2014, 2(3-4): 431-461.

 

[20] Hah Z, Kim H, Youn S. A hierarchically superimposing local refinement method for isogeometric analysis[J]. International Journal of Computational Methods. 2014, 11(05): 1350074.

 

[21] Nguyen-Xuan H, Hoang T, Nguyen V P. An isogeometric analysis for elliptic homogenization problems[J]. Computers & Mathematics with Applications. 2014, 67(9): 1722-1741.

 

[22] Owens A R, Welch J A, Kópházi J, et al. Discontinuous isogeometric analysis methods for the first-order form of the neutron transport equation with discrete ordinate (S N) angular discretisation[J]. Journal of Computational Physics. 2016, 315: 501-535.

 

[23] Langer U, Moore S E, Neumüller M. Space-time isogeometric analysis of parabolic evolution problems[J]. Computer Methods in Applied Mechanics and Engineering. 2016.

 

[24] Schillinger D, Ruthala P K, Nguyen L H. Lagrange extraction and projection for NURBS basis functions: a direct link between isogeometric and standard nodal finite element formulations[J]. International Journal for Numerical Methods in Engineering. 2016.

 

[25] Dufour J, Leclercq S, Schneider J, et al. 3D surface measurements with isogeometric stereocorrelation—Application to complex shapes[J]. Optics and Lasers in Engineering. 2016.

 

[26] Wilhelm M, Dedè L, Sangalli L M, et al. IGS: An IsoGeometric approach for smoothing on surfaces[J]. Computer Methods in Applied Mechanics and Engineering. 2016, 302: 70-89.